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, cilt.179, sa.2, ss.696-721, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 179 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s10957-017-1159-3
  • Dergi Adı: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.696-721
  • Anahtar Kelimeler: Stochastic maximum principle, Regime switching, Stochastic delay equations, Anticipated backward stochastic differential equations, Jump-diffusions, Optimal consumption, 93E20, 91G80, 60J75, DIFFERENTIAL-EQUATIONS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.