In this paper, consideration is given to the normative use of expected-utility theory for the purposes of asset allocation by the trustees of retirement funds. A distinction is drawn between “type-1 prudence”, which relates to deliberate conservatism on the part of actuaries in the setting of assumptions and the determination of model parameters, and “type-2 prudence”, which relates to the risk aversion of the trustees. The intention of the research was to quantify type-2 prudence for the purposes of asset allocation, both for defined-contribution (DC) and defined-benefit (DB) funds. The authors propose new definitions of the objective variables used as the argument of the utility function: one for DC funds and another for DB funds. A new class of utility functions, referred to as the “weighted average relative risk aversion” class is proposed. Practicalities of implementation are discussed. Illustrative results of the application of the method are presented, and it is shown that the proposed approach resolves the paradox of counter-intuitive results found in the literature regarding the sensitivity of the optimal asset allocation to the funding level of a DB fund.

We consider large insurance portfolios consisting of life or disability insurance policies that are assumed independent, conditional on a stochastic process representing the economic–demographic environment. Using the conditional law of large numbers, we show that when the portfolio of liabilities becomes large enough, its value on a δ-year horizon can be approximated by a functional of the environment process. Based on this representation, we derive a semi-analytical approximation of the systematic risk quantiles of the future liability value for a homogeneous portfolio when the environment is represented by a one-factor diffusion process. For the multi-factor diffusion case, we propose two different risk aggregation techniques for a portfolio consisting of large, homogeneous pools. We give numerical results comparing the resulting capital charges with the Solvency II standard formula, based on disability claims data from the Swedish insurance company Folksam.

Retirements from the workforce can be split between those who are forced to retire early specifically for health reasons referred to as ill-health retirements and all other retirements referred to as normal-health retirements. Rates of ill-health retirement increase with age and are higher for females than males. Consequently, the mortality experience of ill-health retirement pensioners will become more important in the future as pension schemes increase their normal retirement age in line with increases in life expectancy and the proportion of women in the workforce and therefore in occupational pension schemes increases. This paper seeks to model the mortality of ill-health retirements from occupational pension schemes in the United Kingdom in the period immediately following retirement (reverse select mortality) and over the longer term (ultimate mortality) allowing for age at retirement. Females experience a longer reverse select period than males and for both males and females the improvement in mortality rates over the reverse select period is greatest at younger ages. Post the reverse select period the effect of age at retirement decreases over time with ultimate mortality rates converging by the mid-eighties for males and females.

In insurance risk theory, dividend and aggregate claim amount are of great research interest as they represent the insurance company’s payments to its shareholders and policyholders, respectively. Since the analyses of these two quantities are performed separately in the literature, the companion paper by Cheung et al. generalised the Gerber–Shiu expected discounted penalty function by further incorporating the moments of the aggregate discounted claims until ruin and the discounted dividends until ruin. While Cheung et al. considered the compound Poisson model with a dividend barrier in which ruin occurs almost surely, the present paper looks at this generalised Gerber–Shiu function under a threshold dividend strategy where the insurer has a positive survival probability. Because the Gerber–Shiu function is only defined for sample paths leading to ruin, we will additionally study the joint moments of the aggregate discounted claims and the discounted dividends without ruin occurring. Some explicit formulas are derived when the individual claim distribution follows a combination of exponentials. Numerical illustrations involving the correlation between aggregate discounted claims and discounted dividends are given. For the case where ruin occurs, we additionally compute the correlations between the time of ruin and the above two quantities.

We develop a Bayesian model for continuous-time incurred but not yet reported (IBNYR) events under four types of secondary data, and show that unreported events, such as claims, have a Poisson distribution with a reduced arrival parameter if event arrivals are Poisson distributed. Using insurance claims as an example of an IBNYR event, we apply Markov chain Monte Carlo (MCMC) to the continuous-time IBNYR claims model of Jewell using Type I and Type IV data. We illustrate the relative stability of the MCMC method versus the Gammoid approximation of Jewell by showing that the MCMC estimates approach their prior parameters, while the Gammoid approximations grow without bound for Type IV data. Moreover, this holds for any distribution that the delay parameter is assumed to follow. Our framework also allows for the computation of posterior confidence intervals for the parameters.

Actuaries often encounter censored and masked survival data when constructing multiple-decrement tables. In this paper, we propose estimators for the cause-specific failure time density using LOESS smoothing techniques that are employed in the presence of left-censored data, while still allowing for right-censored and exact observations, as well as masked causes of failure. The smoothing mechanism is incorporated as part of an expectation-maximisation algorithm. The proposed models are applied to a bivariate African sleeping sickness data set.

This paper shows how the well-known Bornhuetter–Ferguson claims-reserving method can be extended by applying fuzzy methods. The a priori information for the ultimate claims derives from market statistics, organisational data, etc. and might contain vagueness. Likewise, the parameters of the claims development pattern can be vague or are adapted, retrospectively, due to subjective judgement. With the help of fuzzy numbers we develop new predictors for the ultimate claims. Furthermore, we quantify the uncertainty of the ultimate claims for single and aggregated accident years.

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