Taming the beast of uncertainty has been the grand project to which actuaries have dedicated much of their energy and skill over at least the last 50 years – roughly the time since, in Hans Bühlmann's (1989) famous term, “Actuaries of the Second Kind” emerged.

This paper applies cointegration techniques, developed in econometrics to model long-run relationships, to cause-of-death data. We analyze the five main causes of death across five major countries, including USA, Japan, France, England & Wales and Australia. Our analysis provides a better understanding of the long-run equilibrium relationships between the five main causes of death, providing new insights into similarities and differences in trends. The results identify for the first time similarities between countries and genders that are consistent with past studies on the aging processes by biologists and demographers. The insights from biological theory on aging are found to be reflected in the cointegrating relations in all of the countries included in the study.

Auto insurance companies must adapt to ever-evolving regulations and technological progress. Several variables commonly used to predict accidents rates, such as gender and territory, are being questioned by regulators. Insurers are pressured to find new variables that predict accidents more accurately and are socially acceptable. Annual mileage seems an ideal candidate. The recent development in new technologies should induce insurance carriers to explore ways to introduce mileage-based insurance premiums. We use the unique database of a major insurer in Taiwan to investigate whether annual mileage should be introduced as a rating variable in auto third-party liability insurance. We find that annual mileage is an extremely powerful predictor of the number of claims at-fault. The inclusion of mileage as a new variable should, however, not take place at the expense of bonus-malus systems; rather, the information contained in the bonus-malus premium level complements the value of annual mileage. An accurate rating system should therefore include annual mileage and bonus-malus as the two main building blocks, possibly supplemented by the use of other variables like age, territory and engine cubic capacity. While Taiwan has specific characteristics (high traffic density, a mild bonus-malus system and limited compulsory auto coverage), our results are so strong that we can confidently conjecture that they extend to all developed nations.

We analyze optimal consumption and pension insurance during the life time of a consumer using the life cycle model, when the consumer has recursive utility. The relationship between substitution of consumption and risk aversion is highlighted, and clarified by the introduction of this type of preferences. We illustrate how recursive utility can be used to explain the empirical consumption puzzle for aggregates. This indicates a plausible choice for the parameters of the utility function, relevant for the consumer in the life cycle model. Optimal life insurance is considered, as well as the portfolio choice problem related to optimal exposures in risky securities. A major finding is that it is optimal for the typical insurance buyer to smooth adverse shocks to the financial market, unlike what is implied by the conventional model. This has implications for what type of contracts the life and pension insurance industry should offer.

In this paper, a single-factor multi-currency (SFM) capital-asset pricing model (SFM-CAPM) is developed. The advantage in using a single-factor model is that it does not treat currency risks as carrying different weight from investment risks; regardless of its source, risk is measured as variance, and weighted accordingly. The aim of this paper is primarily to give actuaries a way ahead in the use of the single-factor CAPM in a multi-currency world for the purposes of the stochastic modelling of the assets and liabilities of long-term financial institutions, such as pension funds, particularly for the purposes of liability-driven investments and market-consistent valuation, and the application of the model has been designed with that intention. However, it is envisaged that the model will also be of interest to other practitioners. The paper's major original contribution to the literature is its proof that, for a single-factor CAPM to work in a multi-currency world, there is a necessary condition. The theory is applied to two major currencies and two minor currencies, namely the US dollar, the UK pound, the South African rand and the Turkish lira.

A retrospective rating plan, whose insurance premium depends upon an insured's actual loss during the policy period, is a special insurance agreement widely used in liability insurance. In this paper, the design of an optimal retrospective rating plan is analyzed from the perspective of the insured who seeks to minimize its risk exposure in the sense of convex order. In order to reduce the moral hazard, we assume that both the insured and the insurer are obligated to pay more for a larger realization of the loss. Under the further assumptions that the minimum premium is zero, the maximum premium is proportional to the expected indemnity, and the basic premium is the only free parameter in the formula for retrospective premium given by Meyers (2004) and that the basic premium is determined in such a way that the expected retrospective premium equates to the expected indemnity with a positive safety loading, we formally establish the relationship that the insured will suffer more risk for a larger loss conversion factor or a higher maximum premium. These findings suggest that the insured prefers an insurance policy with the expected value premium principle, which is a special retrospective premium principle with zero loss conversion factor. In addition, we show that any admissible retrospective rating plan is dominated by a stop-loss insurance policy. Finally, the optimal retention of a stop-loss insurance is derived numerically under the criterion of minimizing the risk-adjusted value of the insured's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.

We present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses generalized dynamic factor models fitted to the differences in the log-mortality rates. We compare their prediction performance with that of models previously described in the literature, including the traditional static factor model fitted to log-mortality rates. We also construct risk measures using vine-copula simulations, which take into account the dependence between the idiosyncratic components of the mortality rates. The methodology is applied to forecast mortality rates for a population portfolio for the UK and to estimate longevity and mortality risks.