Consumption–investment and reinsurance problem under Markovian regime switching: time-consistent solution

El Houda Bouaicha, N., Chighoub, F. and Pal Majumder, A. ORCID: https://orcid.org/0000-0001-6094-4909 (2025) Consumption–investment and reinsurance problem under Markovian regime switching: time-consistent solution. Communications in Mathematics and Statistics, 13. pp. 1037-1073. ISSN 2194-671X doi: 10.1007/s40304-024-00418-1

Abstract/Summary

This paper presents a characterization of equilibrium in a game theoretic description of discounting stochastic consumption, investment and reinsurance problem, in which the controlled state process evolves according to a multi-dimensional linear stochastic differential equation, when the noise is driven by a Brownian motion under the effect of a Markovian regime switching. The running and the terminal costs in the objective functional, are explicitly depended on some general discount functions, which create the time inconsistency of the considered model. Open-loop Nash equilibrium controls are described through some necessary and sufficient equilibrium conditions as well as a verification result. A state feedback equilibrium strategy is achieved via certain partial differential-difference equation. As an application, we study an investment–consumption and equilibrium reinsurance/new business strategies for some particular cases of power and logarithmic utility functions. A numerical example is provided to demonstrate the efficacy of theoretical results.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/122821
Identification Number/DOI	10.1007/s40304-024-00418-1
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
Publisher	Springer
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