Time-consistent consumption, investment, and proportional reinsurance in market models with Markovian regime switching

El Houda Bouaicha, N. ORCID: https://orcid.org/0000-0001-6094-4909, Chighoub, F. and Pal Majumder, A. ORCID: https://orcid.org/0000-0001-6094-4909 (2025) Time-consistent consumption, investment, and proportional reinsurance in market models with Markovian regime switching. International Journal of Control. ISSN 0020-7179 doi: 10.1080/00207179.2025.2451705

Abstract/Summary

This paper outlines an analysis of equilibrium strategies within a game-theoretic framework addressing discounting stochastic scenarios involving consumption, investment, and reinsurance problems. The controlled state process follows a multi-dimensional linear stochastic differential equation influenced by Brownian motion and Poison jump process under a Markovian regime-switching environment. The objective functional encompasses both running and terminal costs explicitly linked to general discount functions, introducing time inconsistency in the model. Open-loop Nash equilibrium controls are detailed, supported by necessary and sufficient equilibrium conditions and a verification outcome. Furthermore, a state feedback equilibrium strategy is attained through a specific partial differential–difference equation. The study delves into investment consumption and equilibrium, reinsurance/new business strategies, specifically examining power and logarithmic utility functions in select cases. To validate the theoretical findings, a numerical example is presented, demonstrating their efficacy.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/120618
Identification Number/DOI	10.1080/00207179.2025.2451705
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics > Applied Statistics
Publisher	Taylor & Francis
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