Portfolio Safeguard Help

PSG Help Version 2.0

Opera Bug

Contents | Index

• Why Portfolio Safeguard
• Introduction to PSG
  • System Requirements
  • PSG Versions
  • PSG Express Edition
  • PSG License Manager
  • GUROBI
  • Get Started with PSG
    • Run File Environment: Get Started
    • MATLAB Environment: Get Started 
    • C++ Environment: Get Started
  • Main Concepts and Structure of PSG
• Main Objects of PSG
  • Data
    • PSG Matrix
    • PSG Point
    • PSG Vector
    • PSG Parameter
  • Functions
    • Table (List) of Functions
    • Deterministic Functions
      • Table (List) of Deterministic Functions
      • Linear Group
        • Variable (variable)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Linear (linear)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Linear Multiple (linearmulti)
          • Calculation in Run-File Environment
      • Nonlinear Group
        • Polynomial Absolute (polynom_abs)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Component Positive (cvar_comp_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Component Negative (cvar_comp_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Component Absolute  (cvar_comp_abs)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • VaR Component Positive (var_comp_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • VaR Component Negative (var_comp_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Maximum Component Positive (max_comp_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Maximum Component Negative (max_comp_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Maximum Component Absolute (max_comp_abs)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Quadratic (quadratic)
          • Calculation in Run-File Environment using Matrix of Scenarios
          • Calculation in MATLAB Environment using Matrix of Scenarios
        • Square Root Quadratic (sqrt_quadratic)
          • Calculation in Run-File Environment using Matrix of scenarios
          • Calculation in MATLAB Environment using Matrix of scenarios
        • Logistic
          • Calculation in Run-File Environment
        • Logarithms Sum (log_sum)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
      • Cardinality Group
        • Cardinality Positive (cardn_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Cardinality Negative (cardn_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Cardinality (cardn)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Buyin Positive (buyin_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Buyin Negative (buyin_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Buyin (buyin)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Fixed Charge Positive (fxchg_pos)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Fixed Charge Negative (fxchg_neg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Fixed Charge (fxchg)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
      • Deterministic Norms
        • L1 Norm (polynom_abs)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • L2 Norm (lp_norm)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment 
        • Lp Norm (lp_norm)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • L1 Distance (polynom_abs)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • L2 Distance (sqrt_quadratic)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • L-Infinity Norm (max_comp_abs)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Scaled CVaR Norm (cvar_comp_abs)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Gradient
        • Calculation in Run-File Environment
        • Calculation in MATLAB Environment
      • Increment
        • Calculation in Run-File Environment
        • Calculation in MATLAB Environment
    • Scenario Functions
      • Linear Loss and Gain
        • Calculation in Run-File Environment 
      • Difference of two Losses
      • Max Loss
      • Ltranche
        • Calculation in Run-File Environment
      • Recourse
        • Example of Optimization Problem
        • Example of Calculation Problem
      • Sum of Splines Operator
        • Sum of Splines in Optimization
        • Sum of Splines in Calculation
        • Extended Mathematical Definition
          • One Independent Factor
          • Multiple Independent Factors
    • Risk Functions 
      • Table (List) of Risk Functions
      • Average Group
        • Average Loss (avg)
          • Calculation  in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Gain (avg_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Max (avg_max_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Max for Gain (avg_max_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Max Deviation (avg_max_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Max Deviation for Gain (avg_max_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • CVaR Group
        • CVaR (cvar_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR for Gain (cvar_risk_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Normal Independent (cvar_risk_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR for Gain Normal Independent (cvar_risk_ni_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Normal Dependent (cvar_risk_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR for Gain Normal Dependent (cvar_risk_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR Deviation (cvar_dev)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Deviation for Gain (cvar_dev_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment 
        • CVaR Deviation Normal Independent (cvar_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment 
        • CVaR Deviation for Gain Normal Independent (cvar_ni_dev_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Deviation Normal Dependent (cvar_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment 
        • CVaR Deviation for Gain Normal Dependent (cvar_nd_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR for Mixture of Normal Independent (avg_cvar_risk_ni)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR for Gain for Mixture of Normal Independent (avg_cvar_risk_ni_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Deviation for Mixture of Normal Independent (avg_cvar_ni_dev)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Deviation for Gain for Mixture of Normal Independent (avg_cvar_ni_dev_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Max (cvar_max_risk)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Max for Gain (cvar_max_risk_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR Max Deviation (cvar_max_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment 
        • CVaR Max Deviation for Gain (cvar_max_dev_g)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR for Discrete Distribution as Function of Atom Probabilities (pCVaR)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • CVaR for Mixture of Normal Distributions as Function of Mixture Weights (wCVaR_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR2 Risk (cvar2_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR2 Error (cvar2_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR2 Deviation (cvar2_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • VaR Group
        • VaR (var_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR for Gain (var_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Normal Independent (var_risk_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR for Gain Normal Independent (var_risk_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Normal Dependent (var_risk_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR for Gain Normal Dependent (var_risk_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation (var_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation for Gain (var_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation Normal Independent (var_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation for Gain Normal Independent (var_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation Normal Dependent (var_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation for Gain Normal Dependent (var_nd_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR for Mixture of Normal Independent (avg_var_risk_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR for Gain for Mixture of Normal Independent (avg_var_risk_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation for Mixture of Normal Independent (avg_var_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • VaR Deviation for Gain for Mixture of Normal Independent (avg_var_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Maximum Group
        • Maximum (max_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum for Gain (max_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum Deviation (max_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum Deviation for Gain (max_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum CVaR (max_cvar_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum CVaR for Gain (max_cvar_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum CVaR Deviation (max_cvar_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum CVaR Deviation for Gain (max_cvar_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum VaR (max_var_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum VaR for Gain (max_var_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum VaR Deviation (max_var_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Maximum VaR Deviation for Gain (max_var_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Mean Abs Group
        • Mean Absolute Error (meanabs_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Error Normal Independent (meanabs_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Error Normal Dependent (meanabs_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk (meanabs_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk for Gain (meanabs_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk Normal Independent (meanabs_risk_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk for Gain Normal Independent (meanabs_risk_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk Normal Dependent (meanabs_risk_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Risk for Gain Normal Dependent (meanabs_risk_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Deviation (meanabs_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Deviation Normal Independent (meanabs_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Deviation Normal Dependent (meanabs_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Partial Moment Group
        • Partial Moment (pm_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment for Gain (pm_pen_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Normal Independent (pm_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment for Gain Normal Independent (pm_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Normal Dependent (pm_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment for Gain Normal Dependent (pm_pen_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Deviation (pm_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Gain Deviation (pm_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Deviation Normal Independent (pm_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Gain Deviation Normal Independent (pm_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Deviation Normal Dependent (pm_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Gain Deviation Normal Dependent (pm_nd_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Partial Moment Normal Independent (avg_pm_pen_ni)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment 
        • Average Partial Moment for Gain Normal Independent (avg_pm_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Partial Moment Deviation Normal Independent (avg_pm_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Partial Moment Gain Deviation Normal Independent (avg_pm_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two (pm2_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two for Gain (pm2_pen_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Normal Independent (pm2_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two for Gain Normal Independent (pm2_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Normal Dependent (pm2_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two for Gain Normal Dependent (pm2_pen_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation for Loss (pm2_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation for Gain (pm2_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation Normal Independent (pm2_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation for Gain Normal Independent (pm2_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation Normal Dependent (pm2_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Deviation for Gain Normal Dependent (pm2_nd_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Max (pm2_max_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Max for Gain (pm2_max_pen_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Max Deviation (pm2_max_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Partial Moment Two Max Deviation for Gain (pm2_max_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • CDaR Group
        • CDaR (cdar_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CDaR for Gain (cdar_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Maximum (drawdown_dev_max)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Maximum for Gain (drawdown_dev_max_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Average (drawdown_dev_avg)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Average for Gain (drawdown_dev_avg_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CDaR Multiple (cdarmulti_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CDaR for Gain Multiple (cdarmulti_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Maximum Multiple (drawdownmulti_dev_max)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Maximum for Gain Multiple (drawdownmulti_dev_max_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Average Multiple (drawdownmulti_dev_avg)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Drawdown Average for Gain Multiple (drawdownmulti_dev_avg_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Probability Group
        • Probability of Exceedance (pr_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance for Gain (pr_pen_g)
          • Calculationin Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Normal Independent (pr_pen_ni)
          • Calculationin Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance for Gain Normal Independent (pr_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Penalty for Loss Normal Dependent (pr_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Penalty for Gain Normal Dependent (pr_pen_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation  (pr_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation for Gain (pr_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation Normal Independent (pr_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation for Gain Normal Independent (pr_ni_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation Normal Dependent (pr_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation for Gain Normal Dependent (pr_nd_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Probability of Exceedance Normal Independent (avg_pr_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Probability of Exceedance Penalty for Gain Normal Independent (avg_pr_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Probability of Exceedance Deviation Normal Independent (avg_pr_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Multiple (prmulti_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance for Gain Multiple (prmulti_pen_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Multiple Normal Independent (prmulti_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance for Gain Multiple Normal Independent (prmulti_pen_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Multiple Normal Dependent (prmulti_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance for Gain Multiple Normal Dependent (prmulti_pen_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation Multiple (prmulti_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation for Gain Multiple (prmulti_dev_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation Multiple Normal Independent (prmulti_ni_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Probability of Exceedance Deviation Multiple Normal Dependent (prmulti_nd_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Buffered Probability of Exceedance (bpoe)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Standard Group
        • Root Mean Squared Error (st_pen)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Root Mean Squared Error Normal Independent (st_pen_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Root Mean Squared Error Normal Dependent (st_pen_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Risk (st_risk)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Gain (st_risk_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Risk Normal Independent (st_risk_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Gain Normal Independent (st_risk_ni_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Risk Normal Dependent (st_risk_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Gain Normal Dependent (st_risk_nd_g)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Standard Deviation (st_dev)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error (meansquare)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error Normal Independent (meansquare_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error Normal Dependent (meansquare_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Variance (variance)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Utilities Group
        • Exponential Utility (exp_eut)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Exponential Utility Normal Independent (exp_eut_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Exponential Utility Normal Dependent (exp_eut_nd)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Logarithmic Utility (log_eut)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Power Utility (pow_eut)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Error Group
        • Mean Absolute Error (meanabs_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Normal Independent Error (meanabs_ni_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Absolute Normal Dependent Error (meanabs_nd_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error (meansquare_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error Normal Independent (meansquare_ni_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Mean Square Error Normal Dependent (meansquare_nd_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Root Mean Squared Error (st_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Root Mean Squared Error Normal Independent (st_ni_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Root Mean Squared Error Normal Dependent (st_nd_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Koenker and Basset Error (kb_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Rockafellar Error (ro_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Lp Norm Stochastic (lp_stoch_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • CVaR2 Error (cvar2_err)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Pseudo_R2
        • Contributions
      • Distance between Distributions Group
        • Kolmogorov-Smirnov Distance between Two Distributions (ksm_max)
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
        • Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions (ksm_max_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Cvar Kolmogorov-Smirnov Distance between Two Distributions (ksm_cvar)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Cvar Kolmogorov-Smirnov Distance from a Discrete Distribution to a Mixture of Normal Independent Distributions (ksm_cvar_ni)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Average Kolmogorov-Smirnov Distance between Two Distributions (ksm_avg)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
        • Relative Entropy (entropyr)
          • Calculation in Run-File Environment
          • Calculation in MATLAB Environment
      • Log-Likelihood Group
        • Logarithms Exponents Sum (logexp_sum)
          • Binary Logistic Regression
          • Logistic Regression in Run-File Environment
          • Calculation in Run-File Environment 
          • Calculation in MATLAB Environment
  • Problem
    • Optimization Problem
      • Mathematical Optimization Problem Statement
      • Elements of Optimization Problem
        • Objective
        • Constraint
        • Box (of Variables)
      • Solver
      • Value
    • Calculate Problem
• General (Text) Format of PSG
  • Problem Statement in General (Text) Format
    • Objective in General (Text) Format
    • Constraint in Text Format
    • MultiConstraint in Text Format
    • Function in Text Format
    • Sum of Functions in Text Format
    • Box (of Variables) in Text Format
    • Solver in Text Format
    • Value in Text Format
  • Replace Operation in Problem Statement
  • Cycle Replace Operation in Problem Statement
  • Data in General (Text) Format
    • PSG Point in General (Text) Format
    • PSG Matrix in General (Text) Format
      • Matrix of Scenarios
      • Sparse (Packed) Matrix Format
      • Block Operation for Matrix
      • Cut Operation for Matrix
      • CrossValidation Operation for Matrix
      • Cutout Operation for Matrix
      • Takein Operation for Matrix
    • PSG Vector in General (Text) Format
    • PSG Parameter in General (Text) Format
• Run File Environment
  • Quick Start with PSG Run-File
    • Conditional Value-at-Risk minimization
    • Problem in General (Text) Format of PSG
  • Input in Run-File
  • Output in Run-File
• MATLAB Environment
  • Main Concepts of PSG in MATLAB Environment
  • Quick Start with PSG MATLAB
  • Lessons
    • Lesson 1. Create Problem using GUI
    • Lesson 2. Solve Problem Programmatically
    • Lesson 3. Create Problem Programmatically
  • Special PSG MATLAB Subroutines
    • riskprog
    • riskparam
    • riskconstrprog
    • riskconstrparam
    • riskratioprog
    • functionvalue
    • functionsensitivity
    • functionincrement
  • Main Objects of PSG MATLAB
    • Problem Statement in MATLAB
    • PSG Data Objects in MATLAB
      • PSG Matrix in MATLAB
      • PSG PMatrix in MATLAB
      • PSG Vector in MATLAB
      • PSG Point in MATLAB
      • PSG Parameter in MATLAB
    • Optimization Solvers in MATLAB
    • PSG Solution in MATLAB
  • PSG Toolbox GUI
    • Quick Start with PSG Toolbox
    • Main Toolbox Window
    • Problem Statement Window
    • PSG Data Objects Windows in Toolbox
      • PSG Matrix in Toolbox
      • PSG PMatrix in Toolbox
      • PSG Vector in Toolbox
      • PSG Point in Toolbox
      • PSG Parameter in Toolbox
    • Special Subroutines in Toolbox
      • RiskProg in Toolbox
      • RiskConstrProg in Toolbox
    • User Subroutine in Toolbox
    • Keyboard Shortcut in Toolbox
  • mpsg_setpathtoPSG
  • PSG MATLAB Functions
    • Operations with PSG Problems
      • tbpsg_toolbox
      • tbpsg_vars
      • tbpsg_run (mpsg_solver)
      • tbpsg_export_to_workspace
      • tbpsg_problem_importfromtext
      • tbpsg_problem_exporttotext
      • tbpsg_create_user_subroutine
      • tbpsg_function_value
      • tbpsg_function_gradient
      • tbpsg_function_increment
      • tbpsg_loss_values
    • Creation of PSG Data Objects
      • tbpsg_matrix_pack
      • tbpsg_pmatrix_pack
      • tbpsg_vector_pack
      • tbpsg_point_pack
      • tbpsg_parameter_pack
    • Extract Solution Results
      • tbpsg_solution_struct
      • tbpsg_solution
      • tbpsg_isoptimal
      • tbpsg_objective
      • tbpsg_function_data
      • tbpsg_function_names
      • tbpsg_time
      • tbpsg_point_data
      • tbpsg_point_vars
      • tbpsg_optimal_point_data
      • tbpsg_optimal_point_vars
      • tbpsg_constraints_data
      • tbpsg_constraints_vars
      • tbpsg_slack_data
      • tbpsg_dual_data
      • tbpsg_vector_constraint_data
      • tbpsg_vector_dual_data
      • tbpsg_vector_slack_data
      • tbpsg_matrix_data
      • tbpsg_matrix_vars
      • tbpsg_vector_data
  • External Functions Interface
    • External m-functions for Function and Gradient
    • External mex-functions for Function and Gradient
  • PSG Global Parameters
    • psg_suppress_message Global
    • psg_suppress_warning Global
• C++ Environment
  • Quick Start with PSG C++ 
    • Start Working with PSG C++ 
    • Problem Optimization in C++ 
      • Example Problem for C++ Environment
      • Problem Description for C++ Environment
      • Optimization Example Problem with C++
• Error Messages

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