Near optimality conditions in stochastic control of jump diffusion processes

被引：16

作者：

Chighoub, Farid ^{[1
]}

Mezerdi, Brahim ^{[1
]}

机构：

[1] Univ Mohamed Khider, Lab Appl Math, Biskra 07000, Algeria

来源：

SYSTEMS & CONTROL LETTERS | 2011年 / 60卷 / 11期

关键词：

Diffusion with jumps; Maximum principle; Near-optimal control; Adjoint process; MAXIMUM PRINCIPLE; DIFFERENTIAL-EQUATIONS; SUFFICIENT CONDITIONS; NEAR-OPTIMALITY;

D O I：

10.1016/j.sysconle.2011.07.009

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with necessary as well as sufficient conditions for near-optimality of controlled jump diffusion processes. Necessary conditions for a control to be near-optimal are derived, using Ekeland's variational principle and some stability results on the state and adjoint processes, with respect to the control variable. In a second step, we show that the necessary conditions for near-optimality, are in fact sufficient for near-optimality provided some concavity conditions are fulfilled. Finally, as an illustration some examples are solved explicitly. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：907 / 916

页数：10

共 23 条

[1] A maximum principle for stochastic control with partial information [J].

Baghery, Fouzia ;

Oksendal, Bernt .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (03) :705-717

[2] Optimality necessary conditions in singular stochastic control problems with nonsmooth data [J].

Bahlali, K. ;

Chighoub, F. ;

Djehiche, B. ;

Mezerdi, B. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) :479-494

[3]

Bahlali K., 1996, STOCH STOCH REP, V57, P303, DOI DOI 10.1080/17442509608834065

[4] On the stochastic maximum principle in optimal control of degenerate diffusions with lipschitz coefficients [J].

Bahlali, Khaled ;

Djehiche, Boualem ;

Mezerdi, Brahim .

APPLIED MATHEMATICS AND OPTIMIZATION, 2007, 56 (03) :364-378

[5] Necessary and sufficient conditions for near-optimality in stochastic control of FBSDEs [J].

Bahlali, Khaled ;

Khelfallah, Nabil ;

Mezerdi, Brahim .

SYSTEMS & CONTROL LETTERS, 2009, 58 (12) :857-864

[6]

Barles G., 1997, STOCHASTICS STOCHAST, V60, P57

[7] Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging [J].

Becherer, Dirk .

ANNALS OF APPLIED PROBABILITY, 2006, 16 (04) :2027-2054

[8] OPTIMAL-CONTROL OF JUMP PROCESSES [J].

BOEL, R ;

VARAIYA, P .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1977, 15 (01) :92-119

[9] Discrete-time approximation of decoupled Forward-Backward SDE with jumps [J].

Bouchard, Bruno ;

Elie, Romuald .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (01) :53-75

[10]

Clarke F.H, 1983, OPTIMIZATION NONSMOO

← 1 2 3 →