Summary:

This paper proposes a categorisation of the models used in actuarial science. For the purposes of this paper a “model” is defined as a “representation of a real system in the form of a homomorphic system that satisfies or instantiates a theory” about the real system. The purpose of categorising these models is to improve the discipline and enable a discussion of the general principles that should apply to each category of models. It may also highlight the usefulness to actuarial problems of models developed in other disciplines, such as industrial engineering and operations research.

The paper starts by reviewing the literature on the categorisation of models used in the actuarial science. In general, the nature of a model may be categorised either by the process by which it is developed or by the process of application. The mathematical formulation of a model is not in itself a criterion for the classification of the model. The difficulty and importance of accurately defining each category are highlighted in the review, as well as the usefulness of having a particular categorisation. Gaps and uncertainties seem unavoidable.

It is highlighted in the paper that there is a process between the real system and the model which explains how the model is developed from information and theory about the real system and from the judgement or subjective input of the agents involved in the development of the system.

The paper then proposes a new categorisation of models, with the categories as follows:

Descriptive models, which describe historical relationships between the variables modelled;
Predictive models, which may have a mathematically identical form to the descriptive model, but would be re-parameterised from describing a historical situation, to predicting future scenarios;
Fund models, usually used for retirement funds or life funds, are based on the rules governing the fund or the contracts entered into by it;
Control models, which are fund models where certain items of the fund data are treated as control variables and an objective variable is defined in terms of the fund value;
Normative models for making recommendations to a decision-maker;
Decision-making models, which is an application of normative and control models.
A mention is also made to the fact that some of these models are general, while others are specific to the decision-maker’s situation. Finally some examples of actuarial models are given for each category.

http://www.actuarialsociety.org.za/Portals/1/Documents/6dfb7be4-01fa-48c8-a237-b68e3a73d86a.pdf

Summary:

This paper explores the risks faced by South African life insurance companies arising from the provision of investment guarantees in products sold. The current thinking and practice of the larger South African life insurance companies regarding investment guarantees is set out following their responses to a survey around the following key areas:

• The risk that investment guarantees will bite on in-force business;
• Methods used to mange investment-guarantee risk;
• Tools currently used to measure this risk;
• Allowance for this risk in the statutory reserves;
• Investment guarantees in new business;
• Charges to policyholders for the cost of investment guarantees; and
• Issues identified by the participants relevant to investment guarantees.
   

The survey was used to help identify the following four products as the main products with investment guarantees sold in the South African market:

The non-profit immediate annuities, which are generally well-matched in fixed-interest stocks;
The participating immediate annuities, which tend to be invested in balanced portfolios (mixtures of bonds and equities);
The unit-linked savings product with a maturity guarantee, which have financial options that may or may not bite and are invested in balanced portfolios; and
The smoothed-bonus savings product with a maturity guarantee, as it has an additional maturity guarantee that increases over the term of the policy due to the addition of vesting bonus.
The paper shows that it is very difficult to exactly hedge the maturity guarantees in unit-linked and smoothed-bonus business. However, approximate hedges are possible and the paper discusses valuation methodologies that assist in measuring the cost of such hedges.

 The paper also compares existing methods used internationally to price and value life insurance business with investment guarantees, focusing on the use of stochastic models. The different methods of valuation are discussed under the following headings:

• Background: allowing for risk in the model assumptions
• Deterministic approach
• Scenario- or stress-testing
• Stochastic methods based on statistical real-world investment models
• Market-consistent valuation techniques, which include:
• The determination of the actual cost of transferring the risk into the market; and
• The use of a market-consistent stochastic investment model
• Practical issues relating to Monte Carlo techniques
• Comparison of different valuation methods
• Methods of valuation used by South African insurers: feedback from the survey. 

The different allowances for risk within each valuation method and the appropriateness of these allowances when valuing investment guarantees are considered. The stochastic models compared include both statistically based real-world models and market-consistent state-price-deflator or risk-neutral models. Practical issues around the building of such asset–liability stochastic models are briefly discussed.

http://www.actuarialsociety.org.za/Portals/1/Documents/b770f287-589e-4763-8289-a8c4f2e4b3b5.pdf