Date of Award

August 2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Vytaras V. B. Brazauskas

Second Advisor

Wei W. W. Wei

Committee Members

Lei L. W. Wang, Chao C. Z. Zhu, Chudamani C. P. Poudyal

Abstract

The traditional pricing approach in the insurance industry assumes independence among insureds, yet overlooks the complexities of interdependent risk profiles. This dissertation addresses this limitation by proposing a premium pricing model tailored for managing dependent risks, drawing inspiration from conditional tail expectation (CTE) theory. In our model, each individual insured's premium is contingent upon the collective loss surpassing a predefined threshold.

To validate the efficacy of our model, we introduce several key properties to ensure fairness and stability in premium determination among insured individuals, including diversification and monotonicity. Diversification ensures that adding one policyholder to the insured group does not unjustly increase the premiums of others, while monotonicity ensures that others’ premiums do not increase due to the increased riskiness of individual policyholders.

We analyze these properties under various distributional assumptions, such as normal, exponential, and Pareto distributions. By establishing the explicit CTE-induced premium and conducting comprehensive parameter analyses and simulations, we investigate the pricing dynamics under different scenarios, demonstrating the robustness and efficacy of our model.

In conclusion, this study emphasizes the importance of integrating nuanced risk dependencies into insurance pricing models. Our proposed model, rooted in conditional tail expectation theory, not only enhances risk management capabilities but also facilitates more equitable premium determination, thereby enhancing the resilience and stability of the insurance sector. This research lays the groundwork for broader adoption in various real-world applications.

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