On Sharpe-ratio-based Optimal Insurance Design

dc.contributor.advisorJiang, Wenjun
dc.contributor.authorLiu, Jianan
dc.contributor.committeememberSwishchuk, Anatoliy
dc.contributor.committeememberBadescu, Alexandru
dc.description.abstractAs 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).
dc.identifier.citationLiu, J. (2024). On Sharpe-ratio-based optimal insurance design (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgary
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectSharpe ratio
dc.subjectValue ar Risk
dc.subjectTail Value at Risk
dc.subjectOptimal insurance
dc.subjectExpected utility over risk
dc.titleOn Sharpe-ratio-based Optimal Insurance Design
dc.typemaster thesis
thesis.degree.disciplineMathematics & Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.thesis.accesssetbystudentI do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.
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