A limit theorem on maximum value of hedging with a homogeneous filtered value measure (Q2902444)

In incomplete market models there exist, by definition, contingent claims that cannot be hedged perfectly. While it might be possible to find superhedging strategies, they are often too costly to be of practical relevance. Thus, one looks for incomplete hedges with the aim to constrain the hedging error. The paper under review studies optimal hedging of a European-type contingent claim under a dynamic risk measure (a so-called filtered value measure, a concept due to \textit{S. Kusuoka} and \textit{Y. Morimoto} [J. Math. Sci., Tokyo 14, No. 2, 117--156 (2007; Zbl 1146.60006)]) in an incomplete, finite-state market model formulated in discrete time. The main result of the paper describes the asymptotics of the hedging risk, assessed by a filtered value measure, when the market model tends to a continuous-time limit. The limit of the hedging risk can be characterized as a viscosity solution to a Hamilton--Jacobi--Bellman equation.