Control improvement for jump-diffusion processes with applications to finance. (English) Zbl 1242.93141
Summary: 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.
MSC:
| 93E20 | Optimal stochastic control |
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 91E10 | Cognitive psychology |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
Keywords:
jump-diffusion process; control improvement; portfolio optimization; CRRA-utility functionsReferences:
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