Correlations between insurance lines of business: An illusion or a real phenomenon? Some methodological considerations
Greg Taylor*, UNSW Australia; Bernard Wong, UNSW Australia; Benjamin Avanzi, UNSW Australia
This paper is concerned with dependency between business segments in the non-life insurance industry. When considering the business of an insurance company at the aggregate level, dependence structures can have a major impact in several areas of Enterprise Risk Management, such as in claims reserving and capital modelling. The accurate estimation of the diversification benefits related to the dependence structures between lines of business (“LoBs”) is crucial for (i) capital efficiency, as one should avoid holding unnecessarily high levels of capital, and (ii) solvency of the insurance company, as an underestimation, on the other hand, may lead to insufficient capitalisation and safety.There seems to be a great deal of preconception as to how dependent insurance claims should be. Often, presence of dependence is taken as a given and rarely discussed or challenged, perhaps because of the lack of extensive data for public analysis. In this paper, we take a different approach, and consider how much correlation some real data sets actually display (the Meyers-Shi dataset from the USA, and the AUSI dataset from Australia). We develop a simple theoretical framework that enables us to explain how and why correlations can be illusory (and what we mean by that). We show with some real examples that, sometimes, most (if not all) of the correlation can be `explained’ by an appropriate methodology. Two major conclusions stem from our analysis:1. In any attempt to measure cross-LoB correlations, careful modelling of the data needs to be the order of the day. The exercise may not be well served by rough modelling, such as the use of simple chain ladders, and may indeed result in the prescription of excessive risk margins and/or capital margins.2. Such empirical evidence as examined in the paper reveals cross-LoB correlations that vary only in the range zero to very modest. There is little evidence in favour of the high correlation assumed in some jurisdictions. The evidence suggests that these assumptions derived from either poor modelling or a misconception of the cross-LoB dependencies relevant to the purpose to which they are applied.
STATISTICAL TOOLS TO MANAGE LONGEVITY RISK
Ana Debón*, Universitat politècnica de val; Patricia Carracedo, Valencia International University
In recent decades the countries of the world have seen significant changes in the pattern of mortality has resulted in an increase in life expectancy. Although actuaries recognize that live longer is beneficial to all and not to anticipate these events is a problem for those involved to assess overall costs annuities a given portfolio and in particular, the sustainability of a system pensions. Therefore, we analyze the effect these changes have had on the development of models for predicting mortality and mortality indicators.In the view of much of authors who build mortality tables, the model must be adapted to the experience of the country. In particular, trends in mortality in Europe are decreasing, but there are big differences between Easter and Wester countries that is worth analyzing.Finally, it should be noted that the techniques used in practice often differ from the tools developed in academia. The experts on some of these reports tend to simplify the models, the number of indicators selected mortality and presentation of results. This approach, according to some authors and our results may lead to an underestimation of the projected life expectancy and dispersion that may have important implications for insurance companies and pension funds.
Bridging risk measures and classical ruin theory
Jose Garrido*, Concordia University; Wenjun Jiang, Western University
Recent research has investigated possible bridges between ruin theory for the Cramer-Lundberg risk model with insurance risk management. Insurance risk models typically decompose into claim frequency and claim severity components, but also include other elements such as the premium loading. These proposed bridges are characterized by only some elements of the insurance risk process, typically the claim severity. Here we propose new risk measures based on solvency criteria that include all the insurance risk model components.An application to the optimal capital allocation problem serves as an illustrative use of these new risk measures.