The martingale method of shortfall risk minimization in a discrete time market

Volume 39 / 2012

Marek Andrzej Kociński Applicationes Mathematicae 39 (2012), 413-424 MSC: Primary 91G20; Secondary 91B30. DOI: 10.4064/am39-4-2


The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.


  • Marek Andrzej KocińskiKatedra Zastosowań Matematyki
    Wydział Zastosowań Informatyki i Matematyki
    Szkoła Główna Gospodarstwa Wiejskiego w Warszawie
    Nowoursynowska 159
    02-776 Warszawa, Polska

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