Computing anticipatory property in stochastic differential systems

被引:1
作者
Endow, Y [1 ]
机构
[1] Chuo Univ, Dept Ind & Syst Engn, Tokyo 1128551, Japan
关键词
D O I
10.1080/01969720590944258
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
This article concerns computing anticipatory property of stochastic systems, which are characterized by forward and/or backward stochastic differential equations. Since a Pardoux-Peng solution of a Backward Stochastic Differential Equation (BSDE) is required adaptedness to the natural filtration of a standard Brownian motion, it is nonanticipatory in the sense of stochastic calculus. However, the BSDE is solved backwardly with a terminal state and the solution will generally depend on the future state. Hence a system described by Forward and Backward Stochastic Differential Equations (FBSDEs) will be shown to be a strong computing anticipatory system. A stochastic system described by a numerical scheme also has the same property.
引用
收藏
页码:457 / 470
页数:14
相关论文
共 21 条
[1]  
[Anonymous], 1951, MEM AM MATH SOC
[2]  
[Anonymous], THESIS MICHIGAN STAT
[3]   CONJUGATE CONVEX FUNCTIONS IN OPTIMAL STOCHASTIC CONTROL [J].
BISMUT, JM .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1973, 44 (02) :384-404
[4]   PRICING OF OPTIONS AND CORPORATE LIABILITIES [J].
BLACK, F ;
SCHOLES, M .
JOURNAL OF POLITICAL ECONOMY, 1973, 81 (03) :637-654
[5]  
CHEN Z, 2001, RAPPORT RECHERECHE I, V4284, P1
[6]  
Dubois DM, 2000, AIP CONF PROC, V517, P3, DOI 10.1063/1.1291243
[7]   Backward stochastic differential equations in finance [J].
El Karoui, N ;
Peng, S ;
Quenez, MC .
MATHEMATICAL FINANCE, 1997, 7 (01) :1-71
[8]  
Endow Y, 2002, AIP CONF PROC, V627, P139, DOI 10.1063/1.1503678
[9]  
ENDOW Y, 2004, EUR M CYB SYST RES U
[10]  
ENDOW Y, 2003, AIP C P CASYS 03, V718, P236