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Title

Stochastic differential game strategies in the presence of reinsurance and dividend payout.

Authors

Mhlanga, Farai Julius; Galane, Lesiba Charles; Mwareya, Nicholas; Chikodza, Eriyoti; Guambe, Calisto

Abstract

This paper presents and examines a problem in which two insurance companies apply non-proportional reinsurance to control risk. Additionally, each firm pays out dividends. The situation is modelled as a zero-sum stochastic differential game between the two companies. The goal of one company is to maintain business competitive advantage over the other by sustaining or increasing the difference between the respective liquid reserves of the two companies while the second company aims to minimise that difference. A verification theorem is formulated, proved and subsequently employed to derive the saddle point components. For the case of the payoff with a non-zero running cost function, we are able to solve explicitly the differential game. Numerical simulations are presented to illustrate the results as well as the economic interpretation.

Subjects

DIFFERENTIAL games; REINSURANCE; STRATEGY games; COST functions; DIVIDENDS

Publication

Journal of Industrial & Management Optimization, 2023, Vol 19, Issue 5, p1

ISSN

1547-5816

Publication type

Academic Journal

DOI

10.3934/jimo.2022099

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