Ermanno Pitacco

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.

Actuarial models for pricing disability benefits: Towards a unifying approach

Abstract A basic probabilistic multistate structure is defined, which provides the possibility of setting up a systematic set of models for “health insurances” (disability annuities and lump sums, as well as Dread Disease Insurance and Long Term Care annuities). A time-continuous general model is proposed, which allows us to take into consideration a wide range of different policy conditions. Moreover, some particular practical calculation procedures for disability annuities are briefly illustrated and reinterpreted in the framework of multistate modelling.

Health insurance : basic actuarial models

The individual perspective: the need for health insurance.- The insurers perspective: managing risks.- Health insurance products.- Introduction to actuarial aspects.- Actuarial models for sickness insurance.- Actuarial models for disability annuities.

Simulation in Insurance

Simulation methods have gained importance with the rapid progress in computer technology. The aim of this lecture is an introduction to simulation in insurance mathematics. First, the general features of simulation methods are presented and discussed. Then, the main principles of the simulation approach in life and non-life insurance mathematics are illustrated. We will not deal with particular applications; to this purpose, the reader can refer to the bibliography.

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.

Disability Insurance, Numerical Methods

This article describes calculation methods used in actuarial practice for pricing disability annuity products. The following categories are dealt with: inception-annuity models, models based on the probability of being disabled, models based on the expected time spent in disability, implementations of the multistate approach. Keywords: inception rates; prevalence rates; inception-annuity formulae; continuance table method; method of decrement tables; Manchester Unity model; multistate models

Trieste: A Node of the Actuarial Network in the Early 1900s

The scope of the actuarial research in Trieste, especially among the insurance companies operating in Trieste, is described. Particular attention is placed on the period around the turn of the century, namely from the last 1800s to the early 1900s, during which Professor Bronzin proposed his innovative ideas. However, some early contributions dating back to the previous part of the 19th century, as well as selected contributions from the 1920s and the 1930s are also addressed, the latter in particular with regard to the heritage of the early “actuarial school” in Trieste.

Simulation in Actuarial Work. Some Computational Problems

Two simulation problems are discussed and two algorithms are suggested. The first algorithm concerns the simulation of the yearly numbers of claims of a car driver and can be used in the evaluation of a merit — rating system in motor insurance. The second algorithm concerns the simulation of the random survival times of assured lives and can be useful in calculations related both to private and social insurance.