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Shortfall risk minimising strategies in the binomial model: characterisation and convergence

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  • Gino Favero
  • Tiziano Vargiolu

Abstract

In this paper we study the dependence on the loss function of the strategy, which minimises the expected shortfall risk when dealing with a financial contingent claim in the particular situation of a binomial model. After having characterised the optimal strategies in the particular cases when the loss function is concave, linear or strictly convex, we analyse how optimal strategies change when we approximate a loss function with a sequence of suitable loss functions. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:2:p:237-253
    DOI: 10.1007/s00186-006-0083-3
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    References listed on IDEAS

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    1. Ioannis Karatzas & Jaksa Cvitanic, 1999. "On dynamic measures of risk," Finance and Stochastics, Springer, vol. 3(4), pages 451-482.
    2. Marco Schulmerich & Siegfried Trautmann, 2003. "Local Expected Shortfall-Hedging in Discrete Time," Review of Finance, European Finance Association, vol. 7(1), pages 75-102.
    3. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    4. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    5. 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.
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    Cited by:

    1. Nicole Bäuerle & André Mundt, 2009. "Dynamic mean-risk optimization in a binomial model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 219-239, 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. Jungmin Choi & Mattias Jonsson, 2009. "Partial Hedging in Financial Markets with a Large Agent," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(4), pages 331-346.
    5. 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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