INFLUENCE OF EXPECTED PREMIUM ON OPTIMAL REINSURANCE AND INVESTMENT STRATEGY

Date

2024-7-31

Author

Gülveren, Anıl

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This thesis investigates optimal investment and reinsurance strategies aimed at maximizing the expected utility of wealth. Building on foundational work in optimal in vestment and insurance strategy within a diffusion setup, we improve the investment model by incorporating an Ornstein-Uhlenbeck to model the instantaneous return rate of the risky asset. This approach provides a more detailed and realistic representation of market fluctuations, capturing both bull and bear markets compared to the one in literature. We propose two different utility functions, logarithmic utility and exponential utility, to define wealth process whose optimized function is developed using the Hamilton-Jacobi-Bellman (HJB) equation and derive closed-form expressions for the optimal investment and reinsurance decisions. In addition to developing the theoretical model, we conduct extensive sensitivity analysis to illustrate how different financial and insurance parameters influence the optimal strategies. The sensitivity analysis provides critical insights into how variations in parameters such as volatility, risk aversion, and time horizon impact the insurer's decisions. Additionally, we apply real-life insurance claims' severity and frequency data along with the market behaviour on a risky asset observations. Specifically, we find that the optimal investment strategy tends to increase in bullish markets and decrease with higher volatility, reflecting the insurer's need to balance risk and return. The optimal reinsurance strategy exhibits threshold behavior, remaining zero until a certain level of risk aversion is reached, beyond which it increases significantly. By incorporating realistic market dynamics and providing actionable insights, these advancements contribute to more effective risk management and strategic planning in volatile markets, providing a more robust and flexible framework for decision-making.

Subject Keywords

Proportional reinsurance, Utility maximization, Hamilton–Jacobi– Bellman equation, Ornstein-Uhlenbeck Process

URI

https://hdl.handle.net/11511/110889

Collections

Graduate School of Applied Mathematics, Thesis