Penalty Approximation and Analytical Characterization of the Problem of Super-Replication under Portfolio Constraints

Authors

Alain Bensoussan, Université Paris-Dauphine
Nizar Touzi, Centre de Recherche en Economie et Statistique
José Luis Menaldi, Wayne State UniversityFollow

Document Type

Article

Abstract

In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.

Disciplines

Numerical Analysis and Computation | Probability

Comments

The final publication is available at IOS Press through http://content.iospress.com/articles/asymptotic-analysis/asy673

Recommended Citation

Bensoussan A., Touzi N. and Menaldi J.-L. (2005). Penalty approximation and analytical characterization of the problem of super-replication under portfolio constraints, Asymptotic Analysis 41, 311-330.