On Sharpe-ratio-based Optimal Insurance Design
Date
2024-02-08
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Abstract
As an important risk-hedging tool, insurance can increase an individual’s expected utility or reduce her risk exposure. However, pursuing both goals is rarely considered in the literature of insurance contracting. This thesis delves into the optimal insurance design problem by striking a balance between the expected utility and the associated risk. To tackle this objective, we resort to the notion of the Sharpe ratio to identify the optimal contract, which is located on the efficient frontier. The focus of this thesis centers on utilizing Value at Risk (VaR) and Tail Value at Risk (TVaR) as risk measures. We derive parametric forms of the optimal indemnity function in scenarios where a decision maker (DM) seeks to maximize end-of-period expected utility subject to a pre-set acceptable risk level. Since the closed-form or analytical solution for such a contract is rather difficult to derive, we present numerous numerical examples to comprehensively explore various aspects of this methodology. As shown by the results, the Shapre-ratio-based contract is relatively robust except in the Pareto case under VaR preference, and increasing the probability level or risk loading factor adversely affects the ratio. Furthermore, we numerically analyze the popular industrial contract specifically the limited excess-of-loss contract, under the framework of VaR. Our findings reveal that the optimal policy is achieved when the upper limit coverage equals VaR minus the deductible amount. This finding bears a strong resemblance to the optimal contract in our proposed model. The results complement the study of Jiang and Ren (2021).
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Keywords
Sharpe ratio, Value ar Risk, Tail Value at Risk, Optimal insurance, Expected utility over risk
Citation
Liu, J. (2024). On Sharpe-ratio-based optimal insurance design (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.