Variance-Optimal Hedging for the Process Based on Non-Extensive Statistical Mechanics and Poisson Jumps

Abstract

In this study, we consider a minimum-variance hedging problem in an incomplete market, in which the risky asset is driven by the process based on non-extensive statistical mechanics and Poisson jumps. Using the stochastic control theory and backward stochastic differential equation method, we obtain a closed-form solution for the minimum-variance hedging policy.