Volume 7, Issue 2 -

This paper develops a threshold function of the Atlantic Multidecadal Oscillation (AMO) index and allows the effect of AMO index changes over time due to global warming to yield improvements in the forecasts of U.S. hurricane activity. The influence of the threshold effect, the AMO effect, and the global warming effect on Value at Risk and expected shortfall of hurricane risk is also examined. The empirical results of a time-variant threshold Poisson regression model provide an excellent projection for which the forecasting error of average annual U.S. hurricane activity is less than one. We find that the threshold effect and global warming effect dominate the AMO effect. In particular, the global warming effect dominates the AMO effect in extreme hurricane events, and this domination increases over time.

This paper presents a general framework for the capital allocation model that minimizes insurance group risk. The Global Financial Crisis greatly affected insurer management. The enormous losses sustained by American International Group’s derivative subsidiary are still fresh in our minds, and group risk management has recently become a material issue. On facing serious financial distress, an insurance group adopts a methodology wherein it focuses its capital on its material subsidiaries using capital and risk transfer instruments (CRTIs) such as reinsurance, loans, and guarantees. To this end, we model the dependency structure between the parent company and its subsidiaries in terms of the associated assets and liabilities, using some copula functions and calculate the optimal risk transferring ratios. At the same time, we consider the parent company’s limited liability toward its subsidiary and evaluate a put-option value to run off an immaterial subsidiary facing financial distress for the diversification of risk on the whole group. Major findings are that different dependency structures result in different risk transferring ratios and the diversification effect for group risk is different depending on the kind of CRTI.

The Lee–Carter (LC) model, developed in the early 1990s, is internationally used for mortality rate projection and risk evaluation. When the LC model is applied to Japanese death rates, however, the residuals of the logarithm of age-specific death rates reveal a time series correlation, and “undulation” is observed in the residual phase on the age and year axes. Previous studies point out the possibility of a cohort effect in Japanese death rates, and one proposes a modified LC model incorporating the death deferred factor. In this paper, taking previous studies into account, we analyze the residual structure involved in the application of the LC model to Japanese death rates and propose the LC-VAR (LC Vector Autoregressive) model, which is an extended LC model, based on this analysis. In addition, we demonstrate examples of the application of the LC-VAR model to pension liability valuation and pricing single net premiums as well as cover the key points in mortality projections.

In this paper, we investigate the change in mortality rate and its impact on annuity liabilities using the Lee-Carter model. Our findings suggest that the insurer suffers a higher risk of insolvency if macroeconomic factors are used in forecasting mortality rates. A hybrid actuarial model, which consists of both annuity and life insurance, is employed to assess an opportunity for natural hedging. We examine the insurer’s insolvency probability while controlling for impact factors, such as the equity contribution, investment allocation and dividend policy. Insurers – who have both life insurance and annuity liabilities – tend to suffer a balanced, lower financial risk and also tend to be more competitive in the market, thus providing the insurer with a natural hedging opportunity to improve financial stability.

Equity-indexed annuities (EIAs) have generated a great deal of interest since Keyport Life first launched “Key Index” in February 1995. They are considered to be the most innovative products to appear on the market in years. EIAs are, essentially equity-linked deferred annuities which provide the policyholder with a guaranteed accumulation rate on their premium, and also at maturity, benefits from an additional return based on the performance of an equity mutual fund or a family of mutual funds or a stock index, typically of the Standard and Poor’s (S&P500) index, so the customer can profit from the growth of the stock market. Product designs of EIAs can vary, depending on the companies that sell them. In this article, we focus on the pricing of one of the product designs in the market which gives the possibility to surrender their policy before maturity. Such options can be valued using Monte Carlo simulation method proposed for pricing American options but, here, we use the least squares Monte Carlo suggested by Longstaff and Schwartz added to the control variate tool in order to construct efficient estimators. We analyze these equity-linked life insurance contracts under four different models. The frameworks differ from the way we model the price of the fund associated with the contract. The first setting is the usual Black and Scholes model, the second is the environment of jump diffusions, especially a Kou process, the third is the regime switching log normal model (RSLN) developed by Hamilton and the fourth is a mixed of a regime switching and a jump diffusion. The surrender option is priced using the Longstaff and Schwartz methodology.

This article considers the same model as Ramsay (“The Asymptotic Ruin Problem When the Healthy and Sickness Periods Form an Alternating Renewal Process.” Insurance: Mathematics and Economics 3:139–43) modified by the inclusion of the interest rate. Exponential type upper bounds for the ultimate ruin probability are derived by martingale and recursive techniques. To illustrate the results, we consider the cases where the length of sickness period and that of healthy period follow Erlang distribution. We then compare numerically the upper bound derived by each technique.