Pointwise Second-Order Necessary Conditions for Stochastic Optimal Control with Jump Diffusions  

作　　者：Abdelhak Ghoul Mokhtar Hafayed Imad Eddine Lakhdari Shahlar Meherrem 

机构地区：[1]Laboratory of Mathematical Analysis,Probabilities and Optimizations,University of Biskra,Po Box 145,07000 Biskra,Algeria [2]Department of Mathematics,Yasar University,University aven,AgaclıYol No.35-57,Izmir,Turkey

出　　处：《Communications in Mathematics and Statistics》2023年第4期741-766,共26页数学与统计通讯（英文）

摘　　要：In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.

关 键 词：Optimal control Stochastic systems with jumps Pointwise second-order necessary condition Maximum principle Variational equation 

分 类 号：O17[理学—数学]