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Optimal partial hedging in a discrete-time market as a knapsack problem

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  • Peter G. Lindberg

Abstract

We present a new approach for studying the problem of optimal hedging of a European option in a finite and complete discrete-time market model. We consider partial hedging strategies that maximize the success probability or minimize the expected shortfall under a cost constraint and show that these problems can be treated as so called knapsack problems, which are a widely researched subject in linear programming. This observation gives us better understanding of the problem of optimal hedging in discrete time.

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  • Peter G. Lindberg, 2009. "Optimal partial hedging in a discrete-time market as a knapsack problem," Papers 0910.5101, arXiv.org.
    • Handle: RePEc:arx:papers:0910.5101
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    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. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    3. 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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