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.

KEYWORDS:

• Regime-switching model
• indifference pricing
• semi-linear parabolic system
• exponential nonlinearity
• flux-limiter
• positivity preserving

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K61
• 36K65
• 65M06

Acknowledgements

The authors are very grateful to the two reviewers for their valuable comments, suggestions and proposed corrections to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second and the third authors are supported by the Bulgarian National Science Fund under Project DN 12/4 ‘Advanced analytical and numerical methods for nonlinear differential equations with applications in finance and environmental pollution’, 2017.