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1 results

  • Super-replication in stochastic volatility models under portfolio constraints

  • Part of
  • Jakša Cvitanić, Huyên Pham, Nizar Touzi
  • Journal:
    Journal of Applied Probability / Volume 36 / Issue 2 / June 1999
    Published online by Cambridge University Press:
    14 July 2016, pp. 523-545
    Print publication:
    June 1999

  • 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 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.