Four Essays in Equity-Linked Life and Pension Insurance

Abstract

In this dissertation we study three very important types of insurance, equity-linked life insurance with surrender guarantees, pension insurance and the insurance provided by (pension) insurance guarantee funds.<br /> In chapter 2 we study the market consistent valuation of equity linked life insurance contracts, particularly the valuation of a surrender option. In our model the policyholder can surrender exogenously and endogenously. More importantly, we model the realistic perspective that the surrender option value depends on the state of the economy. The state of the economy can represent financial market regimes, macroeconomic regimes or business cycles. The consideration of economic states is an important contribution since equity-linked life insurance contracts are long-dated and in the long run there can occur several structural changes in the economic conditions which considerably affect both the value of the underlying financial portfolio and most importantly the surrender behavior of the policyholder. <br /> Chapter 3 and chapter 4 are concerned with the (re)insurance of pension guarantee funds (PGF). These government imposed pension schemes provide (re)insurance to defined benefit (DB) plan holders in terms of paying pension benefits if the corresponding sponsoring company and the pension fund are insolvent. We study and model solution concepts for pension guarantee funds to better protect policyholders by reducing the risk exposure of their financial guarantee. <br /> We model two solution concepts. In chapter 3 we provide a formal model to compute a risk-based premium paid to the PGF under distress termination, the conventional type of termination, where a pension fund is closed due to the insolvency of the sponsoring company. We incorporate several realistic perspectives and compare our theoretical pricing formula for a sample of the largest US DB plan sponsors. In chapter 4 we study the other type of termination, involuntary termination. Under involuntary termination the PGF terminates a substantially underfunded DB plan. In that case the crucial question is when the PGF should optimally intervene. We determine an optimal timing of intervention in terms of a critical funding ratio of the insured DB pension fund. The basic idea of our model is that the PGF acts in the interest of the beneficiaries and maximizes their expected utility. In addition the PGF protects its financial guarantee by controlling two solvency requirements, the shortfall probability and the expected shortfall of the DB plan.<br /> In chapter 4 the DB plan is modeled more specifically and compared to the other main pension retirement plan, the defined contribution plan (DC plan). The analysis is conducted in an expected utility framework under different preferences by taking an essential tradeoff into account. Specifically, the policyholder faces salary risk in both retirement plans, he faces investment risk only in the DC plan and portability risk, the risk of losing benefits when changing the employer is mostly present in the DB plan. As a means of comparison we take the critical job switching intensity or more intuitively the average number of job moves after which the DC plan is preferred in expected utility terms.