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Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches

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  • Gino Favero

Abstract

We consider the problem of minimizing the shortfall risk when the aim is to hedge a contingent claim in a binomial market model and the initial capital is insufficient for a perfect hedge. This problem has been solved under complete information on the underlying model in [3]. We present two possible solutions to the same problem in the case of incomplete information, namely when the underlying probability measure is unknown. The results obtained can also be applied to other classical problems, such as VaR minimization or maximum loss minimization. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Gino Favero, 2001. "Shortfall risk minimization under model uncertainty in the binomial case: adaptive and robust approaches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 493-503, July.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:3:p:493-503
    DOI: 10.1007/s001860100127
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    Cited by:

    1. Gino Favero & Tiziano Vargiolu, 2006. "Shortfall risk minimising strategies in the binomial model: characterisation and convergence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 237-253, October.
    2. Peter Lindberg, 2010. "Optimal partial hedging in a discrete-time market as a knapsack problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 433-451, December.
    3. Barbara Trivellato, 2009. "Replication and shortfall risk in a binomial model with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 1-26, March.
    4. Peter G. Lindberg, 2009. "Optimal partial hedging in a discrete-time market as a knapsack problem," Papers 0910.5101, arXiv.org.

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