Risk minimization under transaction costs
AbstractWe 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 InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 6 (2002)
Issue (Month): 1 ()
Note: received: March 2000; final version received: February 2001
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Web page: http://www.springerlink.com/content/101164/
Find related papers by 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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- Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
- 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.
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