Affiliations: CEREMADE, Université Paris IX, 75775 Paris cedex 16, France E‐mail: alain.bensoussan@wanadoo.fr | Centre de Recherche en Economie et Statistique and CEREMADE, 15 Bd Gabriel Péri, 92245 Malakoff cedex, France E‐mail: touzi@ensae.fr | Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA E‐mail: jlm@math.wayne.edu
Note: [] Corresponding author.
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.
Keywords: hedging under portfolio constraints, penalization, viscosity solutions
