Superreplication under gamma constraints

H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticle

44 Scopus citations

Abstract

In a financial market consisting of a nonrisky asset and a risky one, we study the minimal initial capital needed in order to superreplicate a given contingent claim under a gamma constraint. This is a constraint on the unbounded variation part of the hedging portfolio. We first consider the case in which the prices are given as general Markov diffusion processes and prove a verification theorem which characterizes the superreplication cost as the unique solution of a quasi-variational inequality. In the context of the Black-Scholes model (i.e., when volatility is constant), this theorem allows us to derive an explicit solution of the problem. These results are based on a new dynamic programming principle for general 'stochastic target' problems.

Original languageEnglish (US)
Pages (from-to)73-96
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume39
Issue number1
DOIs
StatePublished - Aug 1 2000

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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