# Case Study: Retirement Portfolio Selection

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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
——————————————————————–

Dataset 1 113752 100 -3.74178374384 292.48 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Data Solution Matlab Toolbox Data Matlab Matlab Code Data R R Code Data
Dataset 2 113752 100 -0.02226697343924 353.01 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) 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
——————————————————————–

Dataset 1 113752 100 -3.74140546345 450.37 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Data Solution Matlab Toolbox Data Matlab Matlab Code Data R R Code Data
Dataset 2 113752 100 -0.0222384434066 554.95 # of Variables # of Scenarios Objective Value Solving Time, PC 3.14GHz (sec) Environments Run-File Data Solution Matlab Toolbox Data Matlab Matlab Code Data R R Code Data
CASE STUDY SUMMARY
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.