Secondary risks in insurance markets

The first essay studies the optimal insolvency risk of a stock insurer from the perspective of a representative insured. This paper examines how to achieve a suitable insolvency risk level for an average insured by balancing the insolvency risk and the insurance price. The study also sheds light on how competition can possibly shape the insolvency risk level of the insurance industry as insurers strive to provide their customers with the best insurance products. Results show that an optimal insolvency risk level exists for a stock insurer with a fixed-size risk pool. Increasing the size of a stock insurer leads to a higher optimal insolvency probability in a competitive insurance market, which is an unexpected but rational result.; The second essay considers the effects of some state-dependent background risks on individuals' insurance demands. The precautionary motive plays a crucial role in determining people's insurance demands in the presence of these background risks. Adding a zero-mean background risk only to the loss state will make a risk-averse person increase his insurance demand if and only if the person is prudent. However, when the zero-mean background risk is only attached to the no-loss state, it will reduce the person's insurance demand if and only if he is prudent. Meanwhile, considering these state-dependent background risks, a comparison of the relative intensities of prudence is necessary in addition to the relative degrees of risk aversion in order to finally determine the interpersonal comparison of the insurance demand.; The third essay examines how long-term insurance contracts can be designed to insure the risk caused by uncertain insurance needs. In a simple three-period model the uncertain bequest needs are only revealed at a later time and remain the private information of the insured. This essay proposes two equivalent long-term life insurance contracts that are incentive compatible and able to achieve a higher welfare level than the simple strategy of buying insurance after the bequest needs are known. The optimal long-term life insurance contract provides the second best solution to policyholders when no insurance can directly be written on nonverifiable, uncertain life insurance needs.