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Risk minimization under transaction costs

Author

Listed:
  • Paolo Guasoni

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

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.

Suggested Citation

  • Paolo Guasoni, 2002. "Risk minimization under transaction costs," Finance and Stochastics, Springer, vol. 6(1), pages 91-113.
    • 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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    Citations

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    Cited by:

    1. Teemu Pennanen, 2014. "Optimal investment and contingent claim valuation in illiquid markets," Finance and Stochastics, Springer, vol. 18(4), pages 733-754, October.
    2. Yan Dolinsky & Yuri Kifer, 2014. "Risk Minimization for Game Options in Markets Imposing Minimal Transaction Costs," Papers 1408.3774, arXiv.org, revised Jun 2015.
    3. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    4. 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.
    5. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.

    More about this item

    Keywords

    Transaction costs; incomplete markets; risk minimization; coherent risk measures; constraints;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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