The article examines various formulations of the problem of partial hedging of American claims in an arbitrage-free and incomplete market. Market behavior scenarios are modeled by a finite tree without self-intersections. The problems are considered from the seller’s viewpoint without information about buyer behavior. The main emphasis is on simplifying the constraints entering the explicit form of the buyer strategy. We find that in all problems the assumption of completely uncertain stopping time can be replaced with simpler restrictions.
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References
H. Föllmer and P. Leukert, “Quantile hedging,” Finance and Stochastics, 3, No. 3, 251–273 (1999).
V. V. Morozov and A. I. Soloviev, “On optimal partial hedging in discrete markets,” Optimization: A Journal of Mathematical Programming and Operations Research, 62, No. 11, 1403–1418 (2013).
L. Perez-Hernandez, “On the existence of an efficient hedge for an American contingent claim within a discrete time market,” Quantitative Finance, 7, No. 5, 547–551 (2007).
A. A. Novikov, “Hedging of options with a given probability,” Theory of Probability and Its Applications, 43, No. 1, 135–143(1999).
P. Lindberg, “Optimal partial hedging of an American option: shifting the focus to the expiration date,” Mathematical Methods of Operations Research, 75, No. 3, 221–243 (2012).
H. Föllmer and A. Schied, Stochastic Finance: an Fntroduction in Discrete Time, 2 nd ed., Walter de Gruyter, Berlin (2004).
G. B. Dantzig, Linear Programming and Extensions, Princeton University Press (1963).
A. A. Vasin and V. V. Morozov, Game Theory and Models in Mathematical Economics [in Russian], MAKS Press, Moscow (2005).
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Translated from Prikladnaya Matematika i Informatika, No. 44, 2013, pp. 114–124.
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Soloviev, A.I. Partial Hedging of American Claims in a Discrete Market. Comput Math Model 25, 592–601 (2014). https://doi.org/10.1007/s10598-014-9252-z
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DOI: https://doi.org/10.1007/s10598-014-9252-z