Abstract
As a main contribution we present a new approach for studying the problem of optimal partial hedging of an American contingent claim in a finite and complete discrete-time market. We assume that at an early exercise time the investor can borrow the amount she has to pay for the option holder by entering a short position in the numéraire asset and that this loan in turn will mature at the expiration date. We model and solve a partial hedging problem, where the investor’s purpose is to find a minimal amount at which she can hedge the above-mentioned loan with a given probability, while the potential shortfall is bounded above by a certain number of numéraire assets. A knapsack problem approach and greedy algorithm are used in solving the problem. To get a wider view of the subject and to make interesting comparisons, we treat also a closely related European case as well as an American case where a barrier condition is applied.
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Lindberg, P. Optimal partial hedging of an American option: shifting the focus to the expiration date. Math Meth Oper Res 75, 221–243 (2012). https://doi.org/10.1007/s00186-012-0382-9
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DOI: https://doi.org/10.1007/s00186-012-0382-9