Abstract
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.
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