OPTIMAL INSURANCE PROBLEMS UNDER MULTIPLE FRAMEWORKS

Abstract

This dissertation explores the decision-making process individuals undergo when confronted with insurable risks, along with a focus on their choice of an optimal insurance strategy under classical and behavioral economic theories. Using the Expected Utility framework and the Expected Value Premium Principle, we conduct empirical tests to determine optimal retention levels for various insurance forms, including quota-share, stop-loss, and policy-limit contracts. In special cases where actuarial fair premium is assumed, this dissertation provides suggestive evidence that full insurance coverage is often optimal under the expected utility framework. This aligns with classic economic theories, which suggest that individuals aim to maximize their expected utility by eliminating uncertainty through complete insurance coverage. However, generally, real-world decision-making often deviates from this assumption, as people tend to value gains and losses in different ways without necessarily considering maximizing the final utility. Consequently, in this dissertation, we incorporate a more robust alternative theory of choice called the prospect theory, as a descriptive model of decision making under uncertainty. We analyze optimal insurance designs under the Prospect Theory framework, focusing on two reference points: the Status-Quo and Full-Insurance. For each reference point, we estimate the optimal retention levels for quota-share and stop-loss insurance, providing insights into how loss aversion and other behavioral factors influence insurance demand. Furthermore, we include numerical studies and illustrative examples that explore how varying levels of loss aversion, loading factors, and reference points affect the optimal insurance design. In conclusion, this dissertation contributes to a more robust understanding of insurance decision-making, offering practical implications for designing insurance contracts that align with both economic rationality and real-world behavioral tendencies.