Super-replication in stochastic volatility models under portfolio constraints

被引:62
作者
Cvitanic, J
Pham, H
Touzi, N
机构
[1] Columbia Univ, Dept Stat, New York, NY 10027 USA
[2] Univ Marne La Vallee, Equipe Analyse & Math Appl, F-77454 Marne La Vallee, France
[3] Univ Paris 09, CEREMADE, F-75775 Paris, France
关键词
stochastic volatility; portfolio constraints; hedging options; viscosity solutions;
D O I
10.1017/S0021900200017290
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
We study a financial market with incompleteness arising from two sources: stochastic volatility and portfolio constraints. The latter are given in terms of bounds imposed on the borrowing and short-selling of a 'hedger' in this market, and can be described by a closed convex set K. We find explicit characterizations of the minimal price needed to super-replicate European-type contingent claims in this framework. The results depend on whether the volatility is bounded away from zero and/or infinity, and also, on if we have linear dynamics for the stock price process, and whether the volatility process depends on the stock price. We use a previously known representation of the minimal price as a supremum of the prices in the corresponding shadow markets, and we derive a PDE characterization of that representation.
引用
收藏
页码:523 / 545
页数:23
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