Numerical method for optimal portfolio in an exponential utility regime-switching model

ABSTRACT

In this work, we consider a system of weakly coupled semi-linear parabolic equations of optimal portfolio in a regime-switching model in the case of exponential utility function, suggested by A.R. Valdez and T. 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, F. Russo, eds., 2013, pp. 435–449]. First, we establish maximum principle for the differential problem. Then, we construct and analyse negativity preserving, flux limited finite difference schemes. Numerical experiments are discussed.

KEYWORDS:

• Regime-switching model
• semi-linear parabolic equation
• exponential non-linearity
• van Leer flux-limiter
• negativity preserving
• convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 35K51
• 35K65
• 65M06

Acknowledgements

The authors are very thankful for suggestions, hints and remarks from the anonymous reviewers.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is 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.