Asymmetric Density for Risk Claim-Size Data: Prediction and Bimodal Data Applications

A new, flexible claim-size Chen density is derived for modeling asymmetric data (negative and positive) with different types of kurtosis (leptokurtic, mesokurtic and platykurtic). The new function is used for modeling bimodal asymmetric medical data, water resource bimodal asymmetric data and asymmetric negatively skewed insurance-claims payment triangle data. The new density accommodates the “symmetric”, “unimodal right skewed”, “unimodal left skewed”, “bimodal right skewed” and “bimodal left skewed” densities. The new hazard function can be “decreasing–constant–increasing (bathtub)”, “monotonically increasing”, “upside down constant–increasing”, “monotonically decreasing”, “J shape” and “upside down”. Four risk indicators are analyzed under insurance-claims payment triangle data using the proposed distribution. Since the insurance-claims data are a quarterly time series, we analyzed them using the autoregressive regression model AR(1). Future insurance-claims forecasting is very important for insurance companies to avoid uncertainty about big losses that may be produced from future claims.

Risk Analysis of the Copula Dependent Aggregate Discounted Claims with Weibull Inter-Arrival Time

We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent claim amount. We then use the Laplace inversion via the Gaver-Stehfest algorithm to solve numerically the first and second moments, which takes the form of a Volterra integral equation (VIE). We compute the average and variance of the aggregate discounted claims under the Farlie-Gumbel-Morgenstern (FGM) copula and conduct a sensitivity analysis under various Weibull inter-claim parameters and claim-size parameters. The comparison between the equidispersed, overdispersed and underdispersed counting processes shows that when claims arrive at times that vary more than is expected, insured lives can expect to pay higher premium, and vice versa for the case of claims arriving at times that vary less than expected. Upon comparing the Weibull risk process with an equivalent Poisson process, we also found that copulas with a wider range of dependency parameter such as the Frank and Heavy Right Tail (HRT), have a greater impact on the value of moments as opposed to modeling under FGM copula with weak dependence structure.

Applying of the Extreme Value Theory for determining extreme claims in the automobile insurance sector: Case of a China car insurance

According to the Chinese Health Statistics Yearbook, in 2005, the number of traffic accidents was 187781 with total direct property losses of 103691.7 (10000 Yuan). This research aims to fill the gap in the literature by investigating the extreme claim sizes not only for the entire portfolio. This empirical study investigates the behavior of the upper tail of the claim size by class of policyholders.

Prediction region for average claim occurrence rate and average claim size in motor insurance

The third-party motor insurance data from Sweden for 1977 described by Andrews and Herzberg in 1985 contain average claim occurrence rate (Pc) , average claim size (Ca) for category of vehicles specified by the kilometres travelled per year (K), geographical zone (Z), no claims bonus (B) and make of car (M). The categorical variables Z and M may first be represented respectively by the vectors (Z1, Z2, … , Z6) and (M1, M2, … , M8) of binary variables. The variable (Pc, Ca) is next modelled to be dependent on X∗ = (K, Z1, Z2, … , Z6, B, M1, M2, … , M8) via a conditional distribution which is derived from an 18-dimensional powernormal distribution. From the conditional distribution, a prediction region for (Pc, Ca) can be obtained to provide useful information on the possible ranges of average claim occurrence rate and average claim size for a given category of vehicles.

PRACTITIONER SUMMARY Factors Affecting the Outcomes of Legal Claims against Auditors

Maksymov, Pickerd, Lowe, Peecher, and Reffett (2020b) draw insights based on interviews with 27 prominent audit litigation attorneys about the factors affecting the initiation of legal claims against auditors and how such factors affect settlement outcomes. We summarize their key findings and discuss important implications for audit practitioners. Specifically, we focus on the key factors that affect plaintiff attorneys’ willingness to pursue legal claims against auditors, including the merits of the claim, size of alleged economic damages, auditors’ ability to pay, and the expected cost to pursue the claim. We also discuss the reasons why most audit disputes settle (as opposed to resolving at trial) and the factors affecting settlement outcomes. We hope the insights provided enhance audit practitioners’ understanding of litigation and the settlement process to allow them to manage claims in a less intimidated and ultimately more strategic manner.

Estimation of Reinsurance Risk Value Using the Excess of Loss Method

As with any other business that has a risk of any incident in the future, the insurance business also needs protection against the risks that may arise in the company so that the company does not lose. Therefore, the need for anticipation in organizing any claims submitted by the insurance company to Reinsurance Company so that insurance company may assign any or all of the risks to reinsurance companies. In the method of reinsurance excess-of-loss there is a certain retention limits that allow reinsurance companies bear no claims incurred on insurance companies. The results of this study showed the average occurrence of claims and the risks that may be encountered by Reinsurance Company during the period of insurance. The magnitude of the risk assumed by the reinsurer relies on the model claims aggregation formed from individual claim size distribution models and distribution models the number of claims incurred in the period of insurance. Besides the magnitude of risk was also determined from the retention limit of insurance and reinsurance method used.

Measuring Durability of Insurance Company Based on Ruin Probability

In this paper, we present the process of the measuring durability of insurance company, in which, this study focus on the discrete-time under the limited time the company must reserve sufficient initial capital to ensure that probability of ruin does not exceed the given quantity of risk. Therefore the illustration of the minimum initial capital under the specified period for the claim size process to the exponential distribution has explained.

A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums

In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.

Ruin Probability Approximations in Sparre Andersen Models with Completely Monotone Claims

We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation.