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MDP Algorithms for portfolio optimization problems in pure jump markets

Bäuerle, N.; Rieder, U.

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 work. 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.


Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2009
Sprache Englisch
Identifikator DOI: 10.1007/s00780-009-0093-0
ISSN: 0949-2984
URN: urn:nbn:de:swb:90-329167
KITopen ID: 1000032916
Erschienen in Finance and Stochastics
Band 13
Heft 4
Seiten 591-611
Schlagworte Portfolio Optimization, Piecewise Deterministic Markov Processes, Markov Decision Process, Operator Fixed Points, Approximation Algorithms
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