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Partial hedging of American contingent claims in a finite discrete time model

Volume 45 / 2018

Marek Andrzej Kociński Applicationes Mathematicae 45 (2018), 161-180 MSC: Primary 91G20; Secondary 93E20. DOI: 10.4064/am2379-11-2018 Published online: 26 November 2018


The shortfall risk minimization problem for the investor who hedges an American contingent claim is studied. The lower bound for the minimal shortfall risk is obtained by maximizing some function over the set all randomized stopping times. It is proved that in a binomial model this lower bound is equal to the minimal shortfall risk. An example is given where the maximum of the function considered over all pure stopping times is less than the minimal shortfall risk. It is shown that the optimal strategy in a binomial model is obtained by superhedging a contingent claim connected with a randomized stopping time which is a solution of an auxiliary maximization problem. There is a similarity of the results obtained to those for European options.


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

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