Penalty approximation and analytical characterization of the problem of super-replication under portfolio constraints

Alain Bensoussan, Nizar Touzi, José Luis Menaldi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)311-330
Number of pages20
JournalAsymptotic Analysis
Volume41
Issue number3-4
StatePublished - 2005

Keywords

  • Hedging under portfolio constraints
  • Penalization
  • Viscosity solutions

ASJC Scopus subject areas

  • General Mathematics

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