Essays on Defined Benefit Pension Insurance and Participating Life Insurance

Abstract

This dissertation deals with two important types of insurance: defined benefit pension insurance in Chapter 2 and participating life insurance in Chapters 3 and 4.<br /> In Chapter 2, a termination rule based on a critical funding ratio is proposed for a pension guarantee fund (PGF) who considers closing an underfunded pension plan. This ratio is determined by solving an expected utility maximization problem on behalf of plan beneficiaries subject to two constraints designed to preserve the PGF's viability. The first is an upper bound on the PGF's annual intervention probability; the second, a restriction on the expected shortfall of an underfunded pension plan which is not closed. Both too low and too high critical funding ratios hurt beneficiaries' interests, depending on their degree of risk aversion. <br /> In Chapter 3, we study risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism, forcing an insurance company to be liquidated once a solvency threshold is reached before maturity, is imposed by a regulator. The early default regulation affects the contracts' value not only directly via changing the contracts' payment streams but also indirectly via influencing policyholders' surrender behaviors. In this paper, we endogenize surrender risk by assuming a representative policyholder's surrender intensity bounded from below and from above and uncover impacts of the regulation on the policyholder's surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. Finally, we discuss the impacts of the early default regulation and insurance company's investment strategies on the policyholder's surrender behavior as well as on the contract value, which are dependent on policyholder's rationality level.<br /> In Chapter 4, we study the fair valuation of participating life insurance policies while linking surrender risk to mortality risk via a systemic health shock, for example, the smog currently prevalent in Asia. The systemic health shock harms the health of all policyholders in the pool, which consequently alters their surrender behavior. In this paper, we propose two surrender change scenarios as the systemic health shock occurs. As the policyholders become impaired, first, they may sell the policies due to an emergent cash demand; or second, they may become more careful in handling their policies. Besides, we also consider an early default mechanism which is imposed by a regulator to protect the policyholders. By analyzing effects of the systemic health shock on the contract valuation in the two scenarios with and without the early default regulation, we conclude the importance of recognizing the connection between mortality risk and surrender risk and understanding policyholders' surrender reactions on charging a fair contract price for the policy and implementing an efficient early default mechanism.