Control Improvement for Jump-Diffusion Processes with Applications to Finance

Control Improvement for Jump-Diffusion Processes with Applications to Finance We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control π , a new control with a better value. If no improvement is possible, then π 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Control Improvement for Jump-Diffusion Processes with Applications to Finance

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Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9141-1
Publisher site
See Article on Publisher Site

Abstract

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control π , a new control with a better value. If no improvement is possible, then π 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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 1, 2012

References

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