Geodesic
Minimax estimation of value-at-risk under hedging of an American contingent claim in a discrete financial market
Contributions to game theory and management, Tome 9 (2016), pp. 276-286

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The game problems between seller and buyer of an American contingent claim relate to large scale problems because a number of buyer's strategies grows overexponentially. Therefore, decomposition of such games turns out to be a fundamental problem. In this paper we prove the existence of a minimax monotonous (in time) strategy of the seller in a loss minimization problem considering value-at-risk measure of loss. The given result allows to substantially decrease a number of constraints in the original problem and lets us turn to an equivalent mixed integer problem with admissible dimension.
Keywords: decision making under uncertainty, value-at-risk, scenario tree, stopping time, hedging. 
@article{CGTM_2016_9_a9,
     author = {Alexey I. Soloviev},
     title = {Minimax estimation of value-at-risk under hedging of an {American} contingent claim in a discrete financial market},
     journal = {Contributions to game theory and management},
     pages = {276--286},
     publisher = {mathdoc},
     volume = {9},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2016_9_a9/}
}
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Alexey I. Soloviev. Minimax estimation of value-at-risk under hedging of an American contingent claim in a discrete financial market. Contributions to game theory and management, Tome 9 (2016), pp. 276-286. http://geodesic.mathdoc.fr/item/CGTM_2016_9_a9/