The economics of insurance: a review and some recent developments.

The present paper is devoted to different methods of choice under risk in an actuarial setting. The classical expected utility theory is first presented, and its drawbacks are underlined. A second approach based on the so-called distorted expectation hypothesis is then described. It will be seen that the well-known stochastic dominance as well as the stop-loss order have common interpretations in both theories, while defining higher degree stochastic orders leads to different concepts. The aim of this paper is to emphasize the similarities of the two approaches of choice under risk as well as to point out their major differences.Economics; Insurance;

Initial premium, aggregate claims and distortion risk measures in XL reinsurance with reinstatements

With reference to risk adjusted premium principle, in this paper we study excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution. In particular, we focus our study on conditions ensuring feasibility of the initial premium, for example with reference to the limit on the payment of each claim. Comonotonic exchangeability shows the way forward to a more general definition of the initial premium: some properties characterizing the proposed premium are presented.Excess of loss reinsurance; reinstatements; distortion risk measures; initial premium; exchangeability.

Background Uuncertainty and the Demand for Insurance against Insurable Risks

Theory suggests that people facing higher uninsurable background risk buy more insurance against other risks that are insurable. This proposition is supported by Italian cross-sectional data. It is shown that the probability of purchasing casualty insurance increases with earnings uncertainty. This finding is consistent with consumer preferences being characterised by decreasing absolute prudenceInsurance, background risk, prudence

Modelling dynamic choice: Private health insurance in Australia, CHERE Research Report 24

This study investigates the role of dynamic, discrete choice modelling in the context of private hospital insurance in Australia. This is achieved with the use of a unique panel data set of young Australian women ? The Australian Longitudinal Study on Women?s Health (or ALSWH). Very few (if any) private health insurance studies in Australia have used panel data due to the limited availability of longitudinal data sets. Yet panel data allows two important innovations ? it allows a researcher to control for unobserved heterogeneity across individuals and facilitates dynamic modelling that would otherwise require long time series data. Both these innovations are a feature of the dynamic, random effects probit model I propose here. Using the ALSWH data set I find that the choice to purchase private hospital insurance is strongly determined by income, access to hospitals and inertia in choice. I also find family formation, pregnancy, education, exercise levels and country of birth to be significant drivers of choice. Interestingly, I find little evidence of adverse selection in this sample of young women, as those more likely to be insured have higher self-reported health and few chronic conditions. Overall, I find the dynamic specification with state dependence effects provides an important insight into consumer behaviour, with young women exhibiting statistically and economically large amounts of inertia in choice. Women who were in cover in 1996 or 2000 were more likely to be covered in 2003. Conversely, women without cover were unlikely to move into cover despite a wide range of Australian Government incentives. As policy makers consider the future of private health care, researchers must consider dynamic studies as way to fully gauge consumer behaviour.private health insurance, Australia

Investigating the market potential for customised long term care insurance products

Previous economic research into long-term care (LTC) has mainly been focussed on one issue: the reasons why the LTC insurance market has not been successful. In this contribution, we analyse the prospects for a new type of insurance policy, which offers a top-up on the resources already available to the individual. We abstract from most problems inherent in LTC insurance markets and derive premium rates for various types of insurance policies. Generally, we find that the top-up option reduces premium rates considerably, to the point where it might be expected that a substantial number of people would take up policies, were they available

Identifying Volatility Risk Premium from Fixed Income Asian Options

We provide approximation formulas for at-the-money asian option prices to extract volatility risk premium from a joint dataset of bonds and option prices. The dynamic model generates stochastic volatility and a time-varying volatility risk premium, which explicitly depends on the average cross section of bond yields and on the time series behavior of option prices. When estimated using a joint dataset of Brazilian local bonds and asian options, the model generates bond risk premium strongly correlated (89%) with a widely accepted emerging markets benchmark index, and a negative volatility risk premium implying that investors might be using options as insurance in this market. Volatility premium explains a significant portion (32.5%) of bond premium, confirming that options are indeed important to identify risk premium in dynamic term structure models.

Dynamic pricing of general insurance in a competitive market

A model for general insurance pricing is developed which represents a stochastic generalisation of the discrete model proposed by Taylor (1986). This model determines the insurance premium based both on the breakeven premium and the competing premiums offered by the rest of the insurance market. The optimal premium is determined using stochastic optimal control theory for two objective functions in order to examine how the optimal premium strategy changes with the insurer’s objective. Each of these problems can be formulated in terms of a multi-dimensional Bellman equation. In the first problem the optimal insurance premium is calculated when the insurer maximises its expected terminal wealth. In the second, the premium is found if the insurer maximises the expected total discounted utility of wealth where the utility function is nonlinear in the wealth. The solution to both these problems is built-up from simpler optimisation problems. For the terminal wealth problem with constant loss-ratio the optimal premium strategy can be found analytically. For the total wealth problem the optimal relative premium is found to increase with the insurer’s risk aversion which leads to reduced market exposure and lower overall wealth generation