Annamaria Olivieri

Uncertainty in mortality projections: an actuarial perspective

Abstract The use of mortality tables that include a forecast of the future trends of mortality (the so-called “projected tables”) for life insurance valuations is analysed. In particular, annuity and term assurance portfolios are considered. The (systematic) risk inherent in the adoption of a table that might not properly represent future mortality is modelled. Some tools for facing such risk are briefly discussed.

Solvency requirements for pension annuities

This paper deals with solvency requirements for life annuities portfolios and funded pension plans. Particular emphasis is devoted to longevity risk, i.e. the risk arising from uncertainty in future mortality trends. This risk must be faced by insurance companies and pension plans that have guaranteed lifelong payoffs.Solvency is investigated referring to immediate annuities, and hence the so-called decumulation phase is addressed. To assess solvency, assets are compared with the random present value of liabilities. Several requirements are considered, each leading to a required asset level that must be financed both with premiums (or contributions) and capital allocation.

Solvency Requirements for Life Annuities: Some Comparisons

In this paper we investigate rules for assessing the capital required by a life annuity portfolio to meet mortality risks, longevity risk in particular. Risks other than mortality are disregarded. Rules which could be adopted in internal models are discussed. Then a comparison is provided with the requirement emerging from Solvency 2.

Stochastic Models for Disability: Approximations and Applications to Sickness and Personal Accident Insurance

In actuarial practice, the main calculations for insurance covers in the health care area, personal accident and sickness insurance in particular, are commonly based on simplified methods, whose probabilistic assumptions are often not enough clear. In this paper, starting from a rather general structure for the disability process, we show that reasonable approximations lead to the multistate model. Thus, we first show that, since the features of the multistate model allow for several disability degrees, a rigorous modelling for personal accident insurance can be obtained; in this context, risk factors (and hence rating factors) can be represented by an appropriate choice of the transition intensities. Secondly, as the multistate model provides a sound framework for interpreting practical calculation methods used in the health insurance area, we revise some pricing formulae for personal accident and sickness insurance used in practice, so to highlight the main underlying probabilistic assumptions.

Life Tables in Actuarial Models: From the Deterministic Setting to a Bayesian Approach

The mortality dynamics experienced in the latest decades, especially at adult and old ages, has motivated the introduction of major innovations in the modeling of mortality for actuarial applications; such innovations concern, in particular, the representation of the uncertainty relating to aggregate mortality.

Linking Life Insurance Benefits to the Investment Performance

In this chapter we examine life insurance products whose benefit amount depends either on the return on investments, market interest rates, stock-market indexes, or other financial indexes.

Pension Plans: Technical and Financial Perspectives

In this Chapter we examine some features of private pension programmes, namely those arrangements providing a post-retirement income in addition to the public pension. As we will see, a private pension plan can be designed either on an individual or a group basis. Although in the modern forms the funding of benefits is always realized on individual basis, group pension plans allow for a funding arrangement based on solidarity principles. The post-retirement income is the basic benefit of a pension plan; however, several rider benefits can be underwritten, covering risks to which an individual is exposed either before or after retirement.

Finance in life insurance: linking benefits to the investment performance

The life insurance products described in the previous chapters are characterized by fixed benefits (and premiums), i.e. the amount of benefits and premiums is stated at issue.

Life Insurance: Reserving

The insurer’s debt position, which is an obvious implication of the single premium arrangement, must be realized also when other premium arrangements are adopted. This need clearly emerged in Sect. 4.4.1. We recall that an asset accumulation - decumulation process develops, throughout the policy duration, against the insurer’s debt position. A technical tool for assessing the insurer’s debt is provided by the socalled mathematical reserve.

Managing a Portfolio of Risks

Basic ideas concerning risk pooling and risk transfer, presented in Chap. 1, are progressed further in the present Chapter, mainly with the following purposes: