Case study background and problem formulations
Instructions for optimization with PSG Run-File, PSG MATLAB Toolbox, and PSG R.
PROBLEM1: Problem_CVaR_only
Minimize -Linear+Quadratic ( expected portfolio terminal value + regularization)
subject to
Portfolio value = sum(asset values)
Cash outflow = sum(adjustments)
Asset position value dynamics
Lower and upper bounds on asset positions
CVaR(-cash outflow – annuity yield) < -required cash outflow
Box constraints
——————————————————————–
Quadratic = External Quadratic Penalty Function
Box constraints = constraints on individual decision variables
——————————————————————–
| # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
| Dataset 1 | 113752 | 100 | -3.74178374384 | 292.48 | |||
|---|---|---|---|---|---|---|---|
| Environments | |||||||
| Run-File | Data | Solution | |||||
| Matlab Toolbox | Data | ||||||
| Matlab | Matlab Code | Data | |||||
| R | R Code | Data | |||||
| # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
| Dataset 2 | 113752 | 100 | -0.02226697343924 | 353.01 | |||
|---|---|---|---|---|---|---|---|
| Environments | |||||||
| Run-File | Data | Solution | |||||
| Matlab Toolbox | Data | ||||||
| Matlab | Matlab Code | Data | |||||
| R | R Code | Data | |||||
PROBLEM2: Problem_CVaR_plus_monotonicity
Minimize -Linear+Quadratic ( expected portfolio terminal value + regularization)
subject to
Portfolio value = sum(asset values)
Cash outflow = sum(adjustments)
Asset position value dynamics
Lower and upper bounds on asset positions
CVaR(-cash outflow – annuity yield) = 0 (monotonicity constraint)
Box constraints (non-negativity constraints on positions)
——————————————————————–
Quadratic = External Quadratic Penalty Function
Box constraints = constraints on individual decision variables
——————————————————————–
| # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
| Dataset 1 | 113752 | 100 | -3.74140546345 | 450.37 | |||
|---|---|---|---|---|---|---|---|
| Environments | |||||||
| Run-File | Data | Solution | |||||
| Matlab Toolbox | Data | ||||||
| Matlab | Matlab Code | Data | |||||
| R | R Code | Data | |||||
| # of Variables | # of Scenarios | Objective Value | Solving Time, PC 3.14GHz (sec) | ||||
| Dataset 2 | 113752 | 100 | -0.0222384434066 | 554.95 | |||
|---|---|---|---|---|---|---|---|
| Environments | |||||||
| Run-File | Data | Solution | |||||
| Matlab Toolbox | Data | ||||||
| Matlab | Matlab Code | Data | |||||
| R | R Code | Data | |||||
This case study solves the retirement portfolio selection problem. The objective is to maximize discounted terminal wealth of the investor, while maintaining constant cash outflows from the portfolio by selling some portion of assets, over an entire investment horizon. The cash outflow requirements are imposed using CVaR constraints and additionally, by monotonicity constraint on the cash outflows.