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A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions

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Abstract

We consider a stochastic control problem where the system is governed by a non linear stochastic differential equation with jumps. The control is allowed to enter into both diffusion and jump terms. By only using the first order expansion and the associated adjoint equation, we establish necessary as well as sufficient optimality conditions of controls for relaxed controls, who are a measure-valued processes.

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Authors and Affiliations

  1. Laboratory of Applied Mathematics, University Med Khider, P.O. Box 145, Biskra, 07000, Algeria

    Adel Chala

Authors
  1. Seid Bahlali
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  2. Adel Chala
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Correspondence to Adel Chala.

Additional information

This work is Partially supported by PHC Tassili 07MDU705 and Marie Curie ITN, no. 213841-2 and the Algerian PNR project No. 8/u07/857.

Seid Bahlali is deceased (1961–2010).

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Bahlali, S., Chala, A. A General Optimality Conditions for Stochastic Control Problems of Jump Diffusions. Appl Math Optim 65, 15–29 (2012). https://doi.org/10.1007/s00245-011-9143-z

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