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Pay-how-you-drive (PHYD) or usage-based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.
Following the EU Gender Directive, that obliges insurance companies to charge the same premium to policyholders of different genders, we address the issue of calculating solvency capital requirements (SCRs) for pure endowments and annuities issued to mixed portfolios. The main theoretical result is that, if the unisex fairness principle is adopted for the unisex premium, the SCR at issuing time of the mixed portfolio calculated with unisex survival probabilities is greater than the sum of the SCRs of the gender-based subportfolios. Numerical results show that for pure endowments the gap between the two is negligible, but for lifetime annuities the gap can be as high as 3–4%. We also analyze some conservative pricing procedures that deviate from the unisex fairness principle, and find that they lead to SCRs that are lower than the sum of the gender-based SCRs because the policyholders are overcharged at issuing time.
We present a savings plan for retirement that removes risk by fixing a constraint on a life-long pension so that it has an upper and a lower bound. This corresponds to the ideas of Nobel laureate R.C. Merton whose implementation has never been published. We show with an illustration that our proposed practical algorithm reproduces the theoretical results after a savings period of around 30 years by using daily, monthly, weekly or yearly updates of the investment positions. We calculate the percentiles of the final accumulated wealth distribution for the adjusted implementation. In the simulated illustration, we observe that the adjusted values converge to the theoretical values of the percentiles when the frequency of update increases. We conclude that monthly adjustments result in a practical way to implement theoretical results that were obtained under the hypothesis of a continuous process by Donnelly et al. (2015). This method is easy to use in practice by pension savers and fund managers.
Recent interest in voters' anti-incumbent sentiments focuses on generational change as well as public weariness with partisan control of a long duration. Theories on the electoral effects of such behaviors predict partisan cycles that suggest rising hazards of party incumbency. This article provides an analytical framework for examining changes and durations of party control in presidential elections as a discrete point process. We introduce the discrete Weibull distribution for testing contagion in the context of renewal theory and develop the notion of pseudo-periodicity for a binary process. Our findings based on this event history approach confirm the claim that party incumbency engenders rising hazards. The partisan cycles that we identified have a pseudo-period of approximately six to eight presidential terms.
We present a methodology to forecast mortality rates and estimate longevity and mortality risks. The methodology uses generalized dynamic factor models fitted to the differences in the log-mortality rates. We compare their prediction performance with that of models previously described in the literature, including the traditional static factor model fitted to log-mortality rates. We also construct risk measures using vine-copula simulations, which take into account the dependence between the idiosyncratic components of the mortality rates. The methodology is applied to forecast mortality rates for a population portfolio for the UK and to estimate longevity and mortality risks.
Chapter Preview. This chapter presents regression models where the dependent variable is categorical, whereas covariates can either be categorical or continuous. In the first part binary dependent variable models are presented, and the second part is aimed at covering general categorical dependent variable models, where the dependent variable has more than two outcomes. This chapter is illustrated with datasets, inspired by real-life situations. It also provides the corresponding R programs for estimation, which are based on R packages glm and mlogit. The same output can be obtained when using SAS or similar software programs for estimating the models presented in this chapter.
Coding Categorical Variables
Categorical variables measure qualitative traits; in other words, they evaluate concepts that can be expressed in words. Table 3.1 presents examples of variables that are measured in a categorical scale and are often found in insurance companies databases. These variables are also called risk factors when they denote characteristics that are associated with losses.
Categorical variables must have mutually exclusive outcomes. The number of categories is the number of possible response levels. For example, if we focus on insurance policies, we can have a variable such as TYPE OF POLICY CHOSEN with as many categories as the number of possible choices for the contracts offered to the customer.
This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the solvency capital requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the standard model approach. Alternatively, the requirement is then calculated using an internal model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR, we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.
We have investigated the performance of pension schemes of with-profit policies containing a guaranteed minimum rate of return and we have found that the price of the guarantee measured in terms of lost returns is enormous. We use simple simulations rather than complex pricing methods to illustrate that the price of an interest guarantee is high in pension products that are currently commercialised in the market. We have found that the customer loses up to about 0.75% yearly in the rate of return when an interest guarantee is purchased, compared to the return of an equivalent saving strategy with the same risk at the level 95%. This can explain why such arrangements are not widely popular. Our approach can be used to inform clients, who are not experts in modern financial models, the impact of paying for an interest guarantee.
Høgh, Linton and Nielsen (2006) showed that the famous result in the award winning paper of Froot and Stein (1998) is not correct in the sense that their result does not follow from their assumptions. In this paper we show that the economic intuition behind the paper of Froot and Stein (1998) is correct and that their result can be obtained when the market is reformulated in a continuous time setting and modern market theory is employed.
We investigate a concept of multivariate pricing, which includes claim history for more than one line of business and is a generalization of the Bühlmann-Straub model. The multivariate credibility model is extended to allow for the age of claims to influence the estimation of future claims. The model is applied to data from a portfolio of commercial lines of business.
The purpose of the paper is to use the age of claims in the prediction of risks. A dynamic random effects model on longitudinal count data is presented, and estimated on the portfolio of a major Spanish insurance company. The estimated autocorrelation coefficients of stationary random effects are decreasing. A consequence is that the predictive ability of a claim decreases with the lag between the period of risk prediction and the period of occurrence. There is a wide gap between the long term properties of actuarial and real-world experience rating schemes. This gap can be partly filled if the age of claims is taken into account in the actuarial model.
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