Date of Award

May 2022

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Wei Wei

Committee Members

David Spade, Chao Zhu, Vytaras Brazauskas, Lei Wang

Abstract

The majority of the literature about moral hazard focuses only on qualitative studies. If a health insurance plan imposes little copayment on the insured, the insured may be motivated to have more than necessary medical services, which would raise the insurer’s share of cost. This is referred to as moral hazard. Furthermore, the involvement of a third party–healthcare providers adds more complications on moral hazard. Healthcare providers and patients might choose to collaborate to benefit more from insurance reimbursement, which consequently result in unnecessary loss of the insurer. In this dissertation, we attempt to solve these issues and focus on develop optimal insurance coverage from both insurer’s and insured’s perspectives.Many companies promote high-deductible health plans (HDHP) to mitigate moral hazard. This dissertation aims to establish models to analyze the decision-making behaviors from the perspectives of both insurers and insureds. In Chapter 3, we analyze the incentive that people switch from low-deductible health plans (LDHPs) to HDHPs with different deductible and premium to maximize the insured’s profit. In Section 3.4, We apply the idea of prospect theory, and compare the value functions under LDHP and HDHP to help the policyholders make the decision. This research is anticipated to make two folds of contributions. First, it would introduce a theoretical approach to quantify the moral hazard and study the insured’s behavior. Second, it would reveal the optimal insurance design through a two-stage optimization scheme. The optimal strategy would take the interests of both parties into consideration and make the insurance a collaborative game. This would efficiently mitigate the moral hazard issue and further enhance the welfare of the entire society.

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