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Title: Dynamic programming for semi-Markov modulated SDEs
Authors: Azevedo, Nuno
Pinheiro, D.
Pinheiro, S.
Keywords: Stochastic optimal control
Dynamic programming
Semi-Markov processes
Issue Date: 3-Nov-2020
Publisher: Taylor & Francis Online
Citation: Azevedo, N., Pinheiro, D., & Pinheiro, S. (2020). Dynamic programming for semi-Markov modulated SDEs. Optimization: A Journal of Mathematical Programming and Operations Research, (publicado online em 03 novembro 2020). Repositório Institucional UPT.
Abstract: We consider a stochastic optimal control problem with state variable dynamics described by a stochastic differential equation of diffusive type modulated by a semi-Markov process with a finite state space. The time horizon is both deterministic and finite. Within such setup, we provide a detailed proof of the dynamic programming principle and use it to characterize the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We illustrate our results with an application to Mathematical Finance: the generalization of Merton's optimal consumption-investment problem to financial markets with semi-Markov switching.
ISSN: 0233-1934 (Print)
1029-4945 (Electronic)
Appears in Collections:REMIT – Artigos em Revistas Internacionais / Papers in International Journals

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