Essays on insurance demand and pricing under default risk

Paper I, "The Liability Regime of Insurance Pools and Its Impact on Pricing", addresses the pricing of insurance premiums for specific forms of risk sharing in the insurance industry. The implicit diversification effect from this risk sharing on the default risk is discussed in connection with a possible joint liability of the co-insurers. The discussion focuses in particular on the risk-adequate premium in a contingent claims approach under various premises, which incidentally reflects the varying effectiveness of the joint liability mechanism to protect the policyholder from the adverse consequences of insolvencies in the risk sharing arrangement. Paper II, "Sometimes More, Sometimes Less: Prudence and the Diversification of Risky Insurance Coverage", considers in a three-state model the optimal level of insurance coverage for a risk-averse policyholder who can split by assumption the insurance policy, and hence the default risk, between several insurance companies. The results indicate whether more diversification by an increased number of insurers entails normatively more or less insurance coverage and how this depends on the insurers' default correlation as well as the policyholder's degree of prudence. Given a model with a continuous loss distribution, Paper III, "Optimal Management of Counterparty Risk in Reinsurance Contracts", derives optimal strategies for a risk-averse primary insurer to manage the counterparty risk in reinsurance contracts. The range of strategies comprises explicit hedging, diversification with two reinsurers, or a mixture of both. In view of the trade-off between costs and security the results suggest a layering of the reinsurance coverage with a layer-specific application of the different risk management instruments. While Paper II and III rest on the assumption of a non-stochastic loss given default, Paper IV, "Tailing the Tail: Insurance Demand, Default Risk, and a Random Loss Given Default", eases this assumption by introducing a random variable for the loss given default and researches the according effects on the optimal level of insurance coverage. In addition, a distribution of the loss given default is fitted from empirical data referring concurrently to the difficulties involved.