Solving the problem of partial hedging through a dual problem

S. S. Leshchenko

Specialized Educational and Scientific Center – A. N. Kolmogorov boarding School of Lomonosov Moscow State University (Moscow)

Abstract: 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.

UDC: 519.856

Received: 31.10.2022
Accepted: 12.09.2023

DOI: 10.22405/2226-8383-2023-24-3-26-41