“Social Security-Adequacy,Equity, and Progressiveness: A Review of Criteria Based on Experience in Canada and the United States,” Robert L. Brown and Jeffrey Ip,January 2000

Abstract

We consider an optimal dynamic control problem for an insurance company with opportunities of proportional reinsurance and investment. The company can purchase proportional reinsurance to reduce its risk level and invest its surplus in a financial market that has a Black-Scholes risky asset and a risk-free asset. When investing in the risk-free asset, three practical borrowing constraints are studied individually: (B1) the borrowing rate is higher than lending (saving) rate, (B2) the dollar amount borrowed is no more than K > 0, and (B3) the proportion of the borrowed amount to the surplus level is no more than k > 0. Under each of the constraints, the objective is to minimize the probability of ruin. Classical stochastic control theory is applied to solve the problem. Specifically, the minimal ruin probability functions are obtained in closed form by solving Hamilton-Jacobi-Bellman (HJB) equations, and their associated optimal reinsurance-investment policies are found by verification techniques.     

“Social Security—Adequacy,Equity, and Progressiveness: A Review of Criteria Based on Experience In Canada and the United States”, Robert L. Brown,January 2000

Abstract

We consider the valuation of credit default swaps (CDSs) under an extended version of Merton’s structural model for a firm’s corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm’s value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm’s value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation.     

“Statistical Independence and Fractional Age Assumptions”, Gordon E. Willmot,January 1997

Abstract

The People’s Republic of China has experienced substantial growth in insurance demand over the last decade. However, development of the related laws and regulations has not kept pace with the development of the insurance industry there. This paper reports on a pioneering study comparing different statutory reserve, solvency, and early warning systems in a sample of countries and regions in three of the world’s important economic regions–Asia, North America, and Europe. It begins with the construction of a model office applicable to the People’s Republic of China’s regulatory framework and unique market environment. Reserve standards and solvency measurement systems in different supervisory frameworks then are applied to the model office. The results are analyzed as a comparative study of the People’s Republic of China’s total assets required for the reserves and solvency margins under the practices of other jurisdictions. Early warning systems also are discussed.     

“An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets”, Zinoviy Landsman and Michael Sherris,January 2007

Knowledge of strong predictors of mortality and longevity is very important for actuarial science and practice. Earlier studies found that parental characteristics as well as early-life conditions and midlife environment play a significant role in survival to advanced ages. However, little is known about the simultaneous effects of these three factors on longevity. This ongoing study attempts to fill this gap by comparing centenarians born in the United States in 1890–1891 with peers born in the same years who died at age 65. The records for centenarians and controls were taken from computerized family histories, which were then linked to 1900 and 1930 U.S. censuses. As a result of this linkage procedure, 765 records of confirmed centenarians and 783 records of controls were obtained. Analysis with multivariate logistic regression found the existence of both general and gender-specific predictors of human longevity. General predictors common for men and women are paternal and maternal longevity. Gender-specific predictors of male longevity are occupation as a farmer at age 40, Northeastern region of birth in the United States, and birth in the second half of year. A gender-specific predictor of female longevity is the availability of radio in the household according to the 1930 U.S. census. Given the importance of familial longevity as an independent predictor of survival to advanced ages, we conducted a comparative study of biological and nonbiological relatives of centenarians using a larger sample of 1,945 validated U.S. centenarians born in 1880–1895. We found that male gender of centenarian has a significant positive effect on survival of adult male relatives (brothers and fathers) but not female blood relatives. Life span of centenarian siblings-in-law is lower compared to life span of centenarian siblings and does not depend on centenarian gender. Wives of male centenarians (who share lifestyle and living conditions) have a significantly better survival compared to wives of centenarians' brothers. This finding demonstrates an important role of shared familial environment and lifestyle in human longevity. The results of this study suggest that familial background, some early-life conditions and midlife characteristics play an important role in longevity.     

“Actuarial Issues in the Novels of Jane Austen”, Daniel D. Skwire,January 1997

Social security systems for old age have been explicitly studied in a public choice framework for more than 30 years. They illustrate extremely well the problems of allocating economic resources through a system of voting. Despite actuarial interest in state pension systems and despite the actuarial calculations that are needed to understand long-term public choice trends, there is almost no reference to public choice economics in the actuarial pensions literature. It can be argued that pension systems currently provide some of the most significant threats to the long-term budget positions of developed countries, a point that was made in the Nobel Laureate lecture of Professor James Buchanan over 24 years ago. In this article, we look at the costs and benefits that will be faced by different groups of voters as a result of state pension reform in the United Kingdom. The results of this analysis suggest that a majority of the electorate will have a strong financial interest in opposing state pension reform except where reform involves raising retirement ages. These results are in accordance not just with theoretical work but with other empirical work and practical observations.