Efficient finite difference method for optimal portfolio in a power utility regime-switching model

ABSTRACT The focus of the present work is a one-dimensional system of weakly coupled degenerate semi-linear parabolic equations of optimal portfolio in a regime-switching with power utility function, suggested in Valdez and Vargiolu [Optimal portfolio in a regime-switching model, in Proceedings of the Ascona '11 Seminar on Stochastic Analysis, Random Fields and Applications, R.C. Dalang, M. Dozzi, and F. Russo, eds., 2013, pp. 435–449]. We extend the model, deriving a new linear parabolic system for indifference option valuation. Then, we investigate the properties of the solution of the systems. Further, we develop and analyse an adequate, flux limited finite difference discretization, which preserves the typical features of the differential problem solution. Numerical experiments are presented and discussed.

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