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 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.

Description: This is a Fellowship Credit Research Paper. A portfolio of different insurance policies such as temporary, endowment and whole-life insurance policies is studied in a stochastic mortality and interest environment. The first two moments of the present value of the benefits of the portfolio are derived. The riskiness of the portfolio as measured by the variance of the present value of the benefits can be divided into an insurance risk and an investment risk in two different ways. One way leads to a more natural interpretation of the two risk components. A simple portfolio is used to illustrate the results.

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: The investment risk generated by a stochastic interest rate is recognized as often the greatest risk associated with a whole life or retirement policy. Recent research has investigated the mathematics of this risk when the interest rate follows a stochastic process and the time to death is considered to be random. In this paper we focus on the use of the zero coupon bond as an investment instrument to fund a whole life policy. It is unlikely that a company will entirely fund a particular single policy with a zero coupon bond.

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: In this paper we discuss the link between the price of a contingent claim and its replicating strategies. We compute the replicating strategies for some contingent claims when the price of stocks are modeled using either the Wiener process or the Poisson process. These replicating strategies are essential knowledge if one wishes to implement a dynamic trading strategy.

Description: This paper discusses both the theoretical and the application aspects of stress testing in managing enterprise risks. Effective stress testing maximizes the risk adjusted enterprise profit by controlling major risks financial, strategic, operational and hazard upon identifying risk metrics and modeling the correlations. A case study is included for demonstration purposes.

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: This paper explores Indian futures and options market as a market for hedging by equity holders. The authors have tried to examine optimal hedge ratio and hedge efficiency, and to provide empirical evidence from India.