Fitted finite volume method for indifference pricing in an exponential utility regime-switching model

摘要

We consider one-dimensional systems of weakly coupled degenerate semi-linear parabolic equations for buyer's and writer's pricing of European options under regime-switching with exponential utility function. First, we prove a comparison principle and then we establish a maximum principle for the indifference pricing differential problems. The differential problems are solved numerically by fitted finite volume method with second-order of accuracy. We prove the discrete maximum principle and convergence of the numerical solutions in maximum norm. Numerical results, illustrating the theoretical statements are presented and discussed. (C) 2019 Elsevier B.V. All rights reserved.