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Risk minimization under transaction costs

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  • Paolo Guasoni

    ()
    (Bank of Italy, Research Department, Via Nazionale, 91, 00184 Roma, Italy Manuscript)

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    Abstract

    We study the general problem of an agent wishing to minimize the risk of a position at a fixed date. The agent trades in a market with a risky asset, with incomplete information, proportional transaction costs, and possibly constraints on strategies. In particular, this framework includes the problems of hedging contingent claims and maximizing utility from wealth. We obtain a minimization problem on a space of predictable processes with finite variation. Borrowing a technique from Calculus of Variation, on this space we look for a convergence which makes minimizing sequences relatively compact, and risk lower semicontinuous. For a class of convex decreasing risk functionals, we show the existence of optimal strategies. Examples include the problems of shortfall minimization, utility maximization, and minimization ofcoherent risk measures.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 1 ()
    Pages: 91-113

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:1:p:91-113

    Note: received: March 2000; final version received: February 2001
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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Transaction costs; incomplete markets; risk minimization; coherent risk measures; constraints;

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    Cited by:
    1. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.
    2. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.

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