A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

Savku E., Weber G.

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol.179, no.2, pp.696-721, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 179 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s10957-017-1159-3
  • Journal Name: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.696-721
  • Keywords: Stochastic maximum principle, Regime switching, Stochastic delay equations, Anticipated backward stochastic differential equations, Jump-diffusions, Optimal consumption, 93E20, 91G80, 60J75, DIFFERENTIAL-EQUATIONS
  • Middle East Technical University Affiliated: Yes

Abstract

We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence-uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.