# Case Study: Retirement Portfolio Selection

Back to main page

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
——————————————————————–
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)
——————————————————————–