Hedging contingent claims for a large investor in an incomplete market

被引:29
作者
Buckdahn, R [1 ]
Hu, Y
机构
[1] Univ Bretagne Occidentale, Dept Math, F-29285 Brest, France
[2] Univ Clermont Ferrand 2, Lab Math Appl, F-63177 Clermont Ferrand, France
关键词
forward-backward stochastic differential equations; contingent claims; hedging strategy; large investor; constrained portfolios; incomplete markets;
D O I
10.1017/S0001867800008181
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this paper we study the problem of pricing contingent claims for a large investor (i.e. the coefficients of the price equation can also depend on the wealth process of the hedger) in an incomplete market where the portfolios are constrained. We formulate this problem so as to find the minimal solution of forward-backward stochastic differential equations (FBSDEs) with constraints. We use the penalization method to construct a sequence of FBSDEs without constraints, and we show that the solutions of these equations converge to the minimal solution we are interested in.
引用
收藏
页码:239 / 255
页数:17
相关论文
共 11 条
[1]  
[Anonymous], APPL STOCHASTIC ANAL
[2]  
ANTONELLI F, 1993, ANN APPL PROB, V3, P773
[3]  
BUCKDAHN R, 1997, IN PRESS MATH OPER R
[4]  
Cvitani J., 1993, Ann. Appl. Probab., P652
[5]  
Cvitanic J, 1996, ANN APPL PROBAB, V6, P370
[6]   Backward stochastic differential equations in finance [J].
El Karoui, N ;
Peng, S ;
Quenez, MC .
MATHEMATICAL FINANCE, 1997, 7 (01) :1-71
[7]   DYNAMIC-PROGRAMMING AND PRICING OF CONTINGENT CLAIMS IN AN INCOMPLETE MARKET [J].
ELKAROUI, N ;
QUENEZ, MC .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1995, 33 (01) :29-66
[8]   SOLUTION OF FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS [J].
HU, Y ;
PENG, S .
PROBABILITY THEORY AND RELATED FIELDS, 1995, 103 (02) :273-283
[9]  
Ladyzhenskaya A., 1968, TRANSL MATH MONOGR, V23
[10]   SOLVING FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS EXPLICITLY - A 4 STEP SCHEME [J].
MA, J ;
PROTTER, P ;
YONG, JM .
PROBABILITY THEORY AND RELATED FIELDS, 1994, 98 (03) :339-359