Mean-Variance Hedging on Uncertain Time Horizon in a Market with a Jump

By Idris Kharroubi, Thomas Lim, Armand Ngoupeyou. Applied Mathematics and Optimization, 2012

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In this work, we study the problem of mean-variance hedging with a random horizon T∧τ, where T is a deterministic constant and τ is a jump time of the underlying asset price process. We first formulate this problem as a stochastic control problem and relate it to a system of BSDEs with a jump. We then provide a verification theorem which gives the optimal strategy for the mean-variance hedging using the solution of the previous system of BSDEs. Finally, we prove that this system of BSDEs admits a solution via a decomposition approach coming from filtration enlargement theory.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2fbd1aba205379237598a1cba4606bdfb5d08518