Control Improvement for Jump-Diffusion Processes with Applications to Finance

Journal Article · Wed Feb 15 00:00:00 EST 2012 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-011-9141-1· OSTI ID:22043816

Baeuerle, Nicole ^[1]; Rieder, Ulrich ^[2]

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1. Karlsruhe Institute of Technology, Institute for Stochastics (Germany)
2. University of Ulm, Department of Optimization and Operations Research (Germany)

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

• OSTI ID: 22043816
• Journal Information: Applied Mathematics and Optimization, Vol. 65, Issue 1; Other Information: Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
CONTROL
DIFFUSION
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
OPTIMIZATION