Description: Discussion of how to obtain tight upper and lower bounds on E[hX] for a given function h, and a random variable X with three known moments.

Description: This paper presents best upper and lower bounds on the expected value of a reinsurance payment under the terms of a contract written on a random loss with known moments. Bounds on the expected exercise value of a financial option are considered also because the mathematical model used for valuing options is similar to that used in reinsurance net premium calculations. From the Actuarial Research Clearing House ARCH 1990 Vol. 1.

Description: This report describes a simple way to construct a bivariate copula with specified marginals and partially specified dependence. For example, the method allows one to model tail behavior scenarios while holding the core of the joint distribution fixed. An Excel workbook named CopulaExample.xls is provided to illustrate the method, including its use in Monte Carlo simulation.

Description: This paper addresses some pervasive problems in using secondary data in actuarial research. An approach to solving these problems is based on information theory. From Transactions of Society of Actuaries 1995, Vol. 47.

Description: Sometimes, rare things happen and the least expected occurs. Indeed, some events occur once or twice in a lifetime leaving little room to learn from experiences. In financial markets, extreme events, no matter how rare, could have a profound impact on a company or even the whole country. Insurers are also not free from the impact of catastrophic large-scale extreme events. As a result, with pervasive economic and financial revolutions sweeping our world and potential devastative catastrophes, the increasing interest in tail risk management is fuelled by practical issues, including investment downside risk and insurance catastrophe risk. Thus, developing statistical techniques to model extreme investment and insurance losses is certainly a major task for risk managers. the purpose of our paper is to apply moment methods to estimate the joint events such as concurrent extreme investment loss and insurance loss. A novel aspect of this article is that it takes into account the correlation between different assets and insurance lines of business.

Description: This paper employs the theory of real option pricing to address problems in the area of operational risk management. Particularly, it develops a two-stage model to help firms determine the optimal triggers in the event of an influenza pandemic. The first stage proposes a regime-dependent epidemic model to simulate the spread of the virus, depending on whether the firm is active or inactive. The second stage views the reactivation decision as a call option and the suspension decision as a put option, and uses dynamic programming method to determine the optimal switching thresholds.

Description: 1993 SOA Annual Meeting, New York. This session discussed the panelist's approach to actuarial education and training in other countries.

Description: In his original monograph on portfolio selection, Markowitz [1952] discusses the tradeoff between the mean and variance of a portfolio. Since then, especially recently, much attention has been focused on asymmetric distributions to minimize risks with given return goal for investors who have special skewness preferences. To address this issue, this paper extends Krokhmal et al. [2002]’s approach by adding CVaR-like constraints to the traditional portfolio optimization problem. The CVaR optimization technique has the advantage of reshaping either the left or right tail of a distribution while not significantly affecting the other. Specifically, this approach is used to manage the skewness of asset-liability portfolios of financial institutions. In addition, the CVaR-like constraints approach is compared with traditional Markowitz method and some other alternatives such as, the CVaR approach [directly optimize CVaR], the Boyle-Ding approach as well as the mean-absolute deviation [MAD] approach. Numerical analysis provides empirical support for the superiority of CVaR-like constraints approach in terms of skewness improvement of mean-variance portfolios.

Description: This paper examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore the pricing of catastrophe risk bonds requires an incomplete markets setting and this creates special difficulties in the pricing methodology. The paper briefly discusses the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.

Description: This paper describes methods for determining bounds on the price of derivative instruments, such as option on insurance futures, given only market information. From Securitization of Insurance Risk: The 1995 Bowles Symposium, M-FI97-1.