Finance and Stochastics

, Volume 13, Issue 4, pp 591–611

MDP algorithms for portfolio optimization problems in pure jump markets

Article

DOI: 10.1007/s00780-009-0093-0

Cite this article as:
Bäuerle, N. & Rieder, U. Finance Stoch (2009) 13: 591. doi:10.1007/s00780-009-0093-0

Abstract

We consider the problem of maximizing the expected utility of the terminal wealth of a portfolio in a continuous-time pure jump market with general utility function. This leads to an optimal control problem for piecewise deterministic Markov processes. Using an embedding procedure we solve the problem by looking at a discrete-time contracting Markov decision process. Our aim is to show that this point of view has a number of advantages, in particular as far as computational aspects are concerned. We characterize the value function as the unique fixed point of the dynamic programming operator and prove the existence of optimal portfolios. Moreover, we show that value iteration as well as Howard’s policy improvement algorithm works. Finally, we give error bounds when the utility function is approximated and when we discretize the state space. A numerical example is presented and our approach is compared to the approximating Markov chain method.

Keywords

Portfolio optimization Piecewise deterministic Markov processes Markov decision process Operator fixed points Approximation algorithms 

Mathematics Subject Classification (2000)

91B28 93E20 90C39 60G55 

JEL Classification

G11 C61 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für StochastikUniversität Karlsruhe (TH)KarlsruheGermany
  2. 2.Institut für Optimierung und Operations ResearchUniversität UlmUlmGermany

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