Practical Financial Optimization: A Library of GAMS Models

Chapter 6

Dynamic Portfolio Optimization with Stochastic Programming

6.1 Preview

In this chapter we develop the GAMS models for dynamic portfolio optimization using stochastic programming. The development is based on the discussion of Chapter PFO-6. The following models are discussed in this chapter and the GAMS source code for each is given in the associated FINLIB files:

 

 

Stochastic dedication models are based on Section PFO-6.4, and combine the static fixed-income portfolio models with scenario optimization. These models are stochastic extensions of the fixed-income models discussed in Chapter 4.

• StochDedication.gms

• StochDedicationBL.gms

Two-stage and multi-stage stochastic programs are based on Sections PFO-6.5 and PFO-6.6, and extend the scenario models analyzed in Chapter 5 to allow dynamic rebalancing of portfolios as time evolves and new information becomes known.

• TwoStageDeterministic.gms

• TwoStageStochastic.gms

• ThreeStageSPDA.gms

6.2 Dynamic Optimization for Fixed-Income Securities

As a first step towards building stochastic programming models for portfolio optimization we extend the immunization and dedication models from Sections 4.3 and 4.4 to incorporate scenarios. All the models here are built upon the finite scenario set Ω, indexed by l.

6.2.1 Stochastic dedication

We start with Model PFO-6.4.1. This is a stochastic dedication model with an objective function and risk constraints, as given in the put/call framework of Section PFO-5.7.

The model is ...