A stochastic target formulation for optimal switching problems in finite horizon

被引：30

作者：

Bouchard, Bruno ^{[1
,2
]}

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris, France

[2] CREST, Paris, France

来源：

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES | 2009年 / 81卷 / 02期

关键词：

optimal switching; impulse control; stochastic targets; jump diffusion processes; viscosity solutions; comparison principle; PARTIAL-DIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS;

D O I：

10.1080/17442500802327360

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a general optimal switching problem for a controlled diffusion and show that its value coincides with the value of a well-suited stochastic target problem associated to a diffusion with jumps. The proof consists in showing that the Hamilton-Jacobi-Bellman equations of both problems are the same and in proving a comparison principle for this equation. This provides a new family of lower bounds for the optimal switching problem, which can be computed by Monte-Carlo methods. This result has also a nice economical interpretation in terms of a firm's valuation.

引用

页码：171 / 197

页数：27

共 19 条

[1]

[Anonymous], 1981, Point Processes and Queues: Martingale Dynamics

[2]

Bensoussan Alain, 1984, Impulse Control and Quasi-Variational Inequalities

[3] Stochastic targets with mixed diffusion processes and viscosity solutions [J].

Bouchard, B .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2002, 101 (02) :273-302

[4] 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

[5] OPTIMAL SWITCHING IN AN ECONOMIC-ACTIVITY UNDER UNCERTAINTY [J].

BREKKE, KA ;

OKSENDAL, B .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1994, 32 (04) :1021-1036

[6] USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].

CRANDALL, MG ;

ISHII, H ;

LIONS, PL .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67

[7] A GENERAL VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING [J].

DELBAEN, F ;

SCHACHERMAYER, W .

MATHEMATISCHE ANNALEN, 1994, 300 (03) :463-520

[8]

Dixit K., 1994, INVESTMENT UNCERTAIN

[9] A model for investment decisions with switching costs [J].

Duckworth, K ;

Zervos, M .

ANNALS OF APPLIED PROBABILITY, 2001, 11 (01) :239-260

[10]

ELKAROUI N, 1995, SIAM J CONTROL OPTIM, V33, P22

← 1 2 →