Description: It is obvious that the introduction of a deductible has two major effects. The amount paid for every claim will drop, resulting in a lower claim burden for the insurance company. There will also be a drop in claim frequency, leading to a decrease in claim handling expenses. However, it is by no means obvious how the average claim size changes with the introduction of a deductible. In this paper, we will study this question. First, we derive some theoretical results then apply them to concrete distributions.

Description: This paper uses the property-liability insurance companies as a research sample to investigate the relation between the enhancement of cost efficiency and the usage of reinsurance and financial derivatives as risk management tools. The stochastic frontier approach is applied to consider not only the mean of cost efficiency, but also its variance. The sample includes both organizational forms, namely, stock and mutual insurers.

Description: This note develops the optimality of the put option as a hedging strategy. For an investor who owns a stock, he can buy a put option to hedge against the downside risk of the stock price. In this short note, we ask two questions with the hedge strategy of the put option. First, whether the investor is better off with the hedging strategy? Second, if the investor is better off with the hedging strategy, whether it is the optimal hedging plan? Our result shows that in a risk averse world an investor will maximize his utility with buying the put option as a hedge strategy.

Description: Securitization of mortality risks is an alternative risk management tool that may have some advantages over reinsurance. The purpose of this paper is to study mortality-based securities, such as swaps and mortality bonds, and to price the proposed mortality securities. We focus on group life annuity data, although the techniques could be applied to other lines of annuity or life insurance.

Description: This paper investigates the optimal multi-period proportional reinsurance strategy that minimizes the ruin probability of an insurer. Some conditions under which it is optimal to have no reinsurance are derived. Based on these results, a new concept, capital threshold of proportional reinsurance, is introduced. In the case of two periods, a lower bound of the capital threshold of proportional reinsurance is provided. Some economic implications and properties of this new concept are also discussed.

Description: Much of the push for ERM has come from regulators and rating agencies, but it is being applied in internal company decision-making as well. This paper reviews the progress made and the needs still outstanding in two key areas of application: optimal capital level for an insurer and risk-adjusted profitability of business units. The basic conclusion is that progress has been made in these areas, but more is needed. Building models is not emphasized—it will be assumed that a state-of-the art model is available. The emphasis is on using such models in decision-making.

Description: The U.K. Pension Protection Fund (PPF) was established in April 2005 to protect the pensions of members of U.K. private sector defined benefit pension schemes that have insufficient assets and whose corporate sponsor fails. The Fund takes over the pension scheme assets and assumes responsibility for the payment of compensation to the former members of the scheme. The PPF is funded by a levy on the population of eligible schemes. To improve its ERM framework, the PPF has undertaken a reverse stress testing exercise. This analysis provided the organization with new insights into its risk profile, the scenarios leading to the PPF’s potential “failure,” and interactions between these scenarios. This paper discusses the principles and objectives of reverse stress testing in the special case of the PPF and then illustrates the application of complex system science techniques for the purpose of reverse stress testing.

Description: Abstract: The U.K. Pension Protection Fund (PPF) was established in April 2005 to protect the pensions of members of U.K. private sector defined benefit pension schemes that have insufficient assets and whose corporate sponsor fails. The Fund takes over the pension scheme assets and assumes responsibility for the payment of compensation to the former members of the scheme. The PPF is funded by a levy on the population of eligible schemes. To improve its ERM framework, the PPF has undertaken a reverse stress testing exercise. This analysis provided the organization with new insights into its risk profile, the scenarios leading to the PPF’s potential “failure,” and interactions between these scenarios. This paper discusses the principles and objectives of reverse stress testing in the special case of the PPF and then illustrates the application of complex system science techniques for the purpose of reverse stress testing.

Description: This paper examines the problem of hedging foreign exchange risk across multiple countries using currency options. The profit target requirement is formulated as a stochastic constraint in the context of a binomial lattice. Models are presented for European options. In a numerical example, five currency options are selected, allowing for long or short positions, depending on the target value.

Description: This paper illustrates the application of stochastic control methods in managing the risk associated with an insurance business. We present the Hamilton-Jacobi-Bellman HJB equation and demonstrate its use in finding the optimal investment strategy based on some given criteria. Here we consider an insurance business with a fixed amount available for investment in a portfolio consisting of one non-risky asset and one risky asset. The object of the resulting control problem is to determine the investment strategy that minimizes infinite time ruin probability. The existence of a solution to the resulting HJB equation is shown. The relevant verification lemma is not presented in this paper and a numerical algorithm is given instead. Examples applied to exponential claims are also presented.