Equilibrium in a Reinsurance Dynamic Risk Setting: Optimal Portfolio Selection

• Published in: Lobachevskii journal of mathematics Vol. 45; no. 12; pp. 6244 - 6258
• Main Authors: Bazyari, Abouzar, Hosseinzadeh, Hossein
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.12.2024; Springer Nature B.V
• Subjects: Algebra; Analysis; Bellman theory; Dynamic programming; Geometry; Insurance; Insurance (contracts); Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Optimization; Probability Theory and Stochastic Processes; Reinsurance; Risk; optimization problem; 2010 Mathematics Subject Classification: Primary 62P05; Secondary 91B05; Girsanov’s theorem; risk retention level; diffusion approximation process; standard Brownian motion
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224607513

This paper considers the equilibrium in a reinsurance dynamic risk setting to have the optimal portfolio selection for the insurer and reinsurance in a fixed term insurance contract which consists of reinsurance price and risk retention level. The risk process is assumed to be a diffusion approximation process of the classic Cramer–Lundberg model which is perturbed by a Brownian motion with drift. We suppose that both the insurer and reinsurer have constant absolute risk aversion preferences with risk aversion coefficients and study the optimal reinsurance models from the perspective of both the insurer and the reinsurer by maximizing the expected exponential utility of terminal wealth given the information set at time using Hamilton–Jacobi–Bellman equation. To obtain the suitable insurance portfolios for the insurance and reinsurer, we use the principle of dynamic programming. Moreover, the simultaneous problems are presented to our insurance portfolio. Finally, to better illustrate the derived formulas we shall study several examples in details and investigate the effect of parameters of models on our optimization problem as well as the economic meaning behind.