Geodesic
Solving the problem of partial hedging through a dual problem
Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 26-41

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In this paper we consider the problem of partial hedging studied in [20]. In this problem, the risk of shortfall is estimated using a robust convex loss functional $L(\cdot)$. In our work, we formulate a dual problem different from the dual problem in [20], we prove the absence of a duality gap, and also the existence of a solution to the primal and dual problems. In addition, we obtain the results of [20] under weaker assumptions using an approach related to the application of theorems of convex analysis.
Keywords: convex duality, real-valued convex risk measures, robust loss functionals, partial hedging. 
@article{CHEB_2023_24_3_a1,
     author = {S. S. Leshchenko},
     title = {Solving the problem of partial hedging through a dual problem},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {26--41},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2023_24_3_a1/}
}
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S. S. Leshchenko. Solving the problem of partial hedging through a dual problem. Čebyševskij sbornik, Tome 24 (2023) no. 3, pp. 26-41. http://geodesic.mathdoc.fr/item/CHEB_2023_24_3_a1/