Browse Research
Viewing 26 to 50 of 188 results
2021
The concept of risk distribution, or aggregating risk to reduce the potential volatility of loss results, is a prerequisite for an insurance transaction. But how much risk distribution is enough for a transaction to qualify as insurance? This paper looks at different methods that can be used to answer that question and ascertain whether or not risk distribution has been achieved from an actuarial point of view.
2021
This paper demonstrates an approach to apply the lasso variable shrinkage and selection method to loss models arising in actuarial science. Specifically, the group lasso penalty is applied to the GB2 distribution, which is a popular distribution used often in actuarial research nowadays.
2021
The classical credibility theory circumvents the challenge of finding the bona fide Bayesian estimate (with respect to the square loss) by restricting attention to the class of linear estimators of data. See, for example, Bühlmann and Gisler (2005) and Klugman et al. (2008) for a detailed treatment.
2021
Properly modeling changes over time is essential for forecasting and important for any model or process with data that span multiple time periods. Despite this, most approaches used are ad hoc or lack a statistical framework for making accurate forecasts.
2021
In this paper we will analyze the model introduced in Siegenthaler (2017). The author promises to present estimators for the one-year (solvency) as well as the ultimate uncertainty of estimated ultimate claim amounts that neither depend on any claim data nor on the reserving method used to estimate these ultimates. Unfortunately, the model cannot fulfill this promise: it only corrects for some bias in the estimated ultimates.
2021
An excess loss factor is a measure of expected loss that is in excess of a given per-occurrence limit. The National Council on Compensation Insurance (NCCI) uses excess loss factors in its retrospective rating plan as well as in aggregate and class ratemaking.
2021
Because insured losses are positive, loss distributions start from zero and are right-tailed. However, residuals, or errors, are centered about a mean of zero and have both right and left tails. Seldom do error terms from models of insured losses seem normal. Usually they are positively skewed, rather than symmetric. And their right tails, as measured by their asymptotic failure rates, are heavier than that of the normal.
2021
Several approximations for the distribution of aggregate claims have been proposed in the literature. In this paper, we have developed a saddlepoint approximation for the aggregate claims distribution and compared it with some existing approximations, such as NP2, gamma, IG, and gamma-IG mixture.
2021
The concept of bias-variance tradeoff provides a mathematical basis for understanding the common modeling problem of under-fitting vs. overfitting. While bias-variance tradeoff is a standard topic in machine learning discussions, the terminology and application differ from that of actuarial literature. In this paper we demystify the bias-variance decomposition by providing a detailed foundation for the theory.
2021
This paper extends uniform-exposure credibility theory by making quadratic adjustments that take into account the squared values of past observations. This approach amounts to introducing nonlinearities in the framework, or to consider-ing higher-order cross-moments in the computations. We first describe the full parametric approach and, for illustration, we examine the Poisson-gamma and Poisson-Pareto cases.
2021
Risk aggregation is virtually everywhere in insurance applications. Indeed, in the vast majority of situations, insurers are interested in the properties of the sums of the risks they are exposed to, rather than in the stand-alone risks per se. Unfortunately, the problem of formulating the probability distributions of the aforementioned sums is rather involved, and as a rule does not have an explicit solution.
2020
This paper discusses an alternative approach to utilizing and credibility weighting the excess loss information for large account pricing. The typical approach is to analyze the burn costs in each excess layer directly (see Clark 2011, for example). Burn costs are extremely volatile in addition to being highly right skewed, which does not perform well with linear credibility methods, such as Buhlmann-Straub or similar methods (Venter 2003).
2020
The standard method for calculating reserves for permanently injured worker benefits (indemnity and medical) is a combination of adjuster-estimated case reserves and reserves for incurred but not reported claims (IBNR) using a triangle method. There has been some interest in other reserving methodologies based on a calculation of future payments for the expected lifetime of the injured worker using a table of mortality rates.
2020
This paper demonstrates a Bayesian approach for estimating loss costs associated with excess of loss reinsurance programs.
2020
This paper proposes a method to derive paid tail factors using incurred tail factors and historical payout patterns. Traditionally, a ratio of paid-to-incurred losses—and its reciprocal, the conversion factor—may be used to convert payments at a specific maturity to incurred losses, prior to attaching an incurred tail factor. The implied paid tail factor would be the product of the incurred tail factor and the selected conversion factor.
2020
This paper proposes efficient statistical tools to detect which risk factors influence insurance losses before fitting a regres-sion model. The statistical procedures are nonparametric and designed according to the format of the variables commonly encountered in P&C ratemaking: continuous, integer-valued (or discrete) or categorical.
2020
Rating areas are commonly used to capture unexplained geographical variability of claims in insurance pricing. A new method for defining rating areas is proposed using a two-part generalized geoadditive model that models spatial effects smoothly using Gaussian Markov random fields. The first part handles zero/nonzero expenses in a logistic model; the second handles nonzero expenses (on log-scale) in a linear model.
2020
An actuarial approach for calculating a relativity based on geographic diversification is presented. The method models correlation as a function of distance between two exposures, and uses that to calculate a risk margin for each policy. It assumes that any premium provision for a company risk margin is currently allocated in proportion to policy risk-free premium, which results in a uniform risk-loading uprate for all policies.
2019
Split credibility has been used in practice for several decades, though its foundational theory has been investigated only recently. This paper studies the properties of the primary loss and the excess loss in the split experience plan of the National Council on Compensation Insurance (NCCI). We first revisit the claim that the excess loss is more volatile than the total loss.
2019
Very similar modeling is done for actuarial models in loss reserving and mortality projection. Both start with incomplete data rectangles, traditionally called triangles, and model the data by year of origin, year of observation, and lag from origin to observation.
2019
In volume 8, no. 2 of Variance, a technique using actuarial present value was applied to infrastructure service contracts (ISCs) as a way to manage obsolescence in portfolios of fixed, physical capital assets. The theory put forth in that paper was purely deductive and used basic financial mathematics to posit some untested hypotheses.
2019
This paper presents closed-form formulas in order to estimate, based on the historical triangle of ultimate estimates, both the one-year and the total run-off reserve risk.
2019
A Bayesian Markov chain Monte Carlo (MCMC) stochastic loss reserve model provides an arbitrarily large number of equally likely parameter sets that enable one to simulate future cash flows of the liability. Using these parameter sets to represent all future outcomes, it is possible to describe any future state in the model’s time horizon including those states necessary to calculate a cost-of-capital risk margin.
2019
The betting industry has grown significantly but there have been no developments in creating a regulatory framework akin to the EU Solvency and Capital Requirement Directives in the Financial Services. This work derives a modular method to calculate the profit and variance of a portfolio of wagers placed with a bookmaker by subdividing these into bundles according to their likelihood size.
