Finance and Stochastics

, Volume 6, Issue 1, pp 91–113 | Cite as

Risk minimization under transaction costs

  • Paolo Guasoni
Original Paper

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.

Key words:Transaction costs, incomplete markets, risk minimization, coherent risk measures, constraints 
JEL Classification: G12, G13 
Mathematics Subject Classification (1991): 60H30, 62P05, 91B30, 26A45 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Paolo Guasoni
    • 1
  1. 1.Bank of Italy, Research Department, Via Nazionale, 91, 00184 Roma, Italy (e-mail: guasoni@dm.unipi.it) IT

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