Ana M. Pérez-Marín

Time-varying effects in the analysis of customer loyalty

Highlights? We prove that the probability of losing a customer holding multiple contracts in an insurance company fluctuates over time. ? Survival analysis methods with time-varying parameters are used to estimate the probability of customer lapse. ? Customer loyalty after a first cancellation depend on the type of policy retained and the effect of competitors. ? The intensity of the factors explaining customer duration is very high right after a first policy cancellation. ? This approach can be used in a variety of contexts to assess the duration of multiple contracts held by the same customer. Insurance customers usually hold more than one contract with the same insurer. A generalization of classical survival analysis methods is used to examine the risk of losing a customer once an initial insurance policy cancellation has occurred. This method does not assume that the model parameters are fixed over time, but rather that the parameters may fluctuate. Our results suggest that the kind of contracts held by customers and the concurrence of an external competitor strongly influence customer loyalty right after that cancellation, but those factors become much less significant some months later. Our study shows how predictions of the probability of losing a customer can be readjusted and improves the way companies manage business risk.

Recent Mortality Trends in the Spanish Population

Our research deals with the way that calendar time affects mortality patterns in the Spanish population, and how this information can be used to elaborate predictions. A description of the observed mortality evolution has been worked out using data from 1975 to 1993. We have used Heligman-Pollard Law number two to model the evolution of Spanish mortality over the period and using univariate time series analysis, we have obtained a prognosis for years 1994 to 2010.

Testing extreme value copulas to estimate the quantile

Testing weather or not data belongs could been generated by a family of extreme value copulas is difficult. We generalize a test and we prove that it can be applied whatever the alternative hypothesis. We also study the effect of using different extreme value copulas in the context of risk estimation. To measure the risk we use a quantile. Our results have motivated by a bivariate sample of losses from a real database of auto insurance claims. Methods are implemented in R.

Time and distance to first accident and driving patterns of young drivers with pay-as-you-drive insurance.

We conducted a study of approximately 16,000 drivers under the age of 30 that had purchased a pay-as-you-drive insurance policy, where their risk of being involved in a crash was analyzed from vehicle tracking data using a global positioning system. The comparison of novice vs. experienced young drivers shows that vehicle usage differs significantly between these groups and that the time to the first crash is shorter for those drivers with less experience. Driving at night and a higher proportion of speed limit violations reduces the time to the first crash for both novice and experienced young drivers, while urban driving reduces the distance traveled to the first crash for both groups. Gender differences are also observed in relation to the influence of driving patterns on the risk of accident. Nighttime driving reduces the time to the first accident in the case of women, but not for men. The risk of an accident increases with excessive speed, but the effect of speed is significantly higher for men than it is for women among the more experienced drivers.

Performance measurement of pension strategies: a case study of Danish life cycle products

The Danish pension market of life cycle products have expanded considerably since its introduction in the beginning of the millennium. The market is maturing and pensioners have the choice between a wide area of different products. It is therefore about time that financial insurance technology is developed to guide the performance measurement of available products. In this paper we develop a simple first version of such a method and we investigate life cycle products recommended on the web of the four biggest commercial Danish pension companies on one day in February 2007. All considered products are outperformed by trivial benchmark products with constant stock proportion over time. Our approach is the following: for each life cycle product we first find a trivial benchmark product with the same long term risk and then we compare the long term return of the two equivalent products. We primarily consider value at risk and tail value at risk as risk measures, but we also include a study where the fair value of an interest guarantee is used as risk measure. We consider both long term mean returns and long term median returns. We hope that our new method will be regarded as a first step towards a scientifically based ranking of the quality of pension products.

Random Forests for Uplift Modeling: An Insurance Customer Retention Case

Models of customer churn are based on historical data and are used to predict the probability that a client switches to another company. We address customer retention in insurance. Rather than concentrating on those customers with high probability of leaving, we propose a new procedure that can be used to identify the target customers who are likely to respond positively to a retention activity. Our approach is based on random forests and can be useful to anticipate the success of marketing actions aimed at reducing customer attrition. We also discuss the type of insurance portfolio database that can be used for this purpose.

Do not pay for a Danish interest guarantee. The law of the triple blow

Abstract 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.

Uplift Random Forests

Conventional supervised statistical learning models aim to achieve high accuracy in predicting the value of an outcome measure based on a number of input measures. However, in many applications, some type of action is randomized on the observational units. This is the case, for example, in treatment/control settings, such as those usually encountered in marketing and clinical trial applications. In these situations, we may not necessarily be interested in predicting the outcome itself, but in estimating the expected change in the outcome as a result of the action. This is precisely the idea behind uplift models, which, despite their many practical applications, have received little attention in the literature. In this article, we extend the state-of-the-art research in this area by proposing a new approach based on Random Forests. We perform carefully designed experiments using simple simulation models to illustrate some of the properties of the proposed method. In addition, we present evidence on a dataset pertaining to a large Canadian insurer on a customer retention case. The results confirm the effectiveness of the proposed method and show favorable performance relative to other existing uplift modeling approaches.

Long-run savings and investment strategy optimization

We focus on automatic strategies to optimize life cycle savings and investment. Classical optimal savings theory establishes that, given the level of risk aversion, a saver would keep the same relative amount invested in risky assets at any given time. We show that, when optimizing lifecycle investment, performance and risk assessment have to take into account the investors risk aversion and the maximum amount the investor could lose, simultaneously. When risk aversion and maximum possible loss are considered jointly, an optimal savings strategy is obtained, which follows from constant rather than relative absolute risk aversion. This result is fundamental to prove that if risk aversion and the maximum possible loss are both high, then holding a constant amount invested in the risky asset is optimal for a standard lifetime saving/pension process and outperforms some other simple strategies. Performance comparisons are based on downside risk-adjusted equivalence that is used in our illustration.

Multiplicative Hazard Models for Studying the Evolution of Mortality

ABSTRACT Almost all over the world, decreasing mortality rates and increasing life expectancy have led to greater interest in estimating and predicting mortality. Here we describe some of the pitfalls which can result from the use of the standardised mortality ratio (SMR) while evaluating the development of mortality over time, in particular when SMRs are applied to insurance portfolios varying dramatically over time. Although an excellent comparative study of a single-figure index for a number of countries was recently done by Macdonald et al. (1998), we advocate care when attempting to extend this type of method to insurance data. Here we promote the use of genuine multiplicative modelling such as in Felipe et al. (2001), who compared the mortality rates in Denmark and Spain. The starting point for our study was the two-dimensional mortality estimator of Nielsen & Linton (1995), which considers mortality as a function of chronological time and age. From the principle of marginal integration (see Nielsen & Linton, 1995, and Linton et al., 2003), estimators of the multiplicative model can be obtained from this two-dimensional estimator. An application of the method is provided for mortality data of the United States of America, England & Wales, France, Italy, Japan and Russia.