1,720,987 research outputs found
A quantitative analysis on the effect of COVID-19 in a private health insurance plan expenditure
No full textThis paper explores the effect of COVID-19 on health care expenditure using data from a private Health Insurance Plan (HIP). As well known, at the beginning of the COVID-19 pandemic, governments had to rely on Non-Pharmaceutical Interventions against the spread of the virus. However, the stringency of lockdowns differed across space and time as governments had to adjust their strategy dynamically to the country-specific development of the crisis. These strategies have strongly changed the policyholders' behavior; however, after this period, a fundamental question is whether the policyholder behavior will return to a status quo (i.e. in traditional care delivery). We analyze these effects using a "pre-post" quantitative study using longitudinal data collected from 2017 to 2021. We consider as a consumption measure the health care expenditure amount within several types of health services, coming from a group of insured persons, followed overtime every quarter, and separating the effect per gender and age. Moving in this direction, the purpose of our contribution is to investigate if the traditional actuarial approach for assessing the loss cost, based on the Generalized Linear Models, could predict the effect on the health care expenditure due to COVID-19 and the capacity to which a HIP can anticipate these uncertainties. Our results provide a comprehensive picture of the different effects of COVID-19 on the health services offered by the HIP, as well as on the behavior ofpolicyholders during and after the pandemic period
A Review on Statistical and Probabilistic Models for the Control of Insurance Companies
No full textThe problem of evaluating the solvency of insurance companies is tackled by means of a non-parametric statistical model, constructed using decision-tree techniques. The model is tested on a sample of Italian non-life insurance companies and its performance over the test period compared with those of linear and quadratic parametric models. In the last part a probabilistic model is proposed focused on classical Risk-Theory and implemented using simulation techniques
An Application of Beta Binomial GAMLSS for the Estimate of Surrender Rates
No full textThis paper deals with the estimate of surrender rate with explanatory variables by a Generalized Linear Model for Location, Scale, and Shape (GAMLSS) where the response variable is assumed Beta Binomial. In actuarial practice and literature, the Binomial Generalized Linear Model is frequently used to get an estimate of surrender rates per policy count conditional to policy and policyholder features. We suggest a regressive model based on a Beta Binomial assumption of the response variable. Beta Binomial is a discrete random variable that differs from binomial because the probability of success at each of n trials is not fixed, but beta distributed. Beta Binomial random variable is fit to model binomial phenomena where the probability of success is not fixed but is inferred from data. Beta Binomial random variable has greater variance and skewness than a Binomial random variable with the same mean, because in the Beta Binomial approach the uncertainty about what the true probability is, is taken into account. This uncertainty makes values far from mean more plausible. Finally, the Beta Binomial does not belong to the exponential family. For this reason, a GAMLSS model is used to get parameter estimates
A Quantile Regression approach for the analysis of the diversification in non-life premium risk
No full textThis paper concerns the study of the diversification effect involved in a portfolio of non-life policies priced via traditional
premium principles when individual pure premiums are calculated via Quantile Regression. Our aim is to use Quantile
Regression to estimate the individual conditional loss distribution given a vector of rating factors. To this aim, we make
a comparison of the outcomes obtained via Quantile Regression with the widely used industry standard method based on
generalized linear models. Then, considering a specific premium principle, we calculate individual pure premium by means
of a specific functional of the conditional loss distribution, the standard deviation. We determine the portfolio risk margin
according to the Solvency 2 framework and then we allocate it over each policy in a way consistent with his/her riskiness.
Indeed, considering a portfolio of heterogeneous policies, we determine the individual reduction of the safety loading, due to
the diversification, and we measure the risk contribution of each individual
On a Fair Value Model for Partecipating Life Insurance Policies
No full textThe aim of this paper is to analyze both the term structure of interest and mortality rates role for evaluating a fair value of a life insurance business. In particular, a fair value accounting impact on reserve evaluations is discussed comparing a traditional deterministic model based on local rules for an Italian balance sheet calculation and a stochastic one based on a diffusion process for both mortality and financial risks. As proposed by IAS Board we will separate the embedded derivatives from their host contracts, so the fair value of a traditional life insurance contract would be expressed as the value of four components: the basic contract, the participation option, the option to annuitise and the surrender option. A numerical application to a traditional Italian life insurance policy is discussed
The influence of gender and age in driving ability: an analysis of average and extreme behaviours
No full textIn 2012, the European Court of Justice introduced the ban on differentiating car insurance premiums for gender to avoid
gender inequality. This paper deals with a gender analysis of driving ability by investigating the relationship between gender
and the relative total claim amount in Motor Third Party Liability insurance, also considering the effect of age. Leveraging a
two-part model based on parametric quantile regression, we want to investigate the average behaviour of drivers and their tail
behaviour in order to highlight the importance of dispersion and the impact of largest claims. As a consequence, the purpose
of our contribution is to study how gender and age can influence the entire probability distribution of the insurance claim with
a particular focus on the quantiles with high probability levels, which are very important indicators to determine the effective
riskiness of a driver.We apply our model to an Australian insurance dataset; our results suggest that men are in general riskier
in terms of both average and tail behaviour
Il Fair value di contratti di assicurazione sulla vita: analisi dell'effetto sul bilancio della compagnia di assicurazione.
No full textPricing Critical Illness Insurance from Prevalence Rates: Gompertz versus Weibull
No full textThe pricing of a Critical Illness insurance requires specific and detailed insur- ance data on healthy and ill lives. However, where the Critical Illness insurance market is small or national commercial insurance data needed for premium esti- mates is unavailable, national health statistics can be a viable starting point for insurance ratemaking purposes, even if such statistics cover the general popu- lation, are aggregate and are reported at irregular intervals. To develop a Critical Illness insurance pricing model structured on a multiple state continuous and time- inhomogeneous Markov chain and based on national statistics, we do three things: First, assuming that the mortality intensity of healthy and ill lives is modeled by two parametrically different Weibull hazard functions, we provide closed formu- las for transition probabilities involved in the multiple state model we propose. Second, we use a data set that allows us to assess the accuracy of our multiple state model as a good estimator of incidence rates under the Weibull assumption applied to mortality rates. Third, the Weibull results are compared to correspond- ing results obtained by substituting two parametrically different Gompertz models for the Weibull models of mortality rates, as proposed in Baione and Levantesi (2014). This enables us to assess which of the two parametric models is the supe- rior tool for accurately calculating the multiple state model transition probabilities and assessing the comparative efficiency of Weibull and Gompertz as methods for pricing Critical Illness insurance
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