No abstract

Nowadays, insurance contract reserves for coupled lives are considered jointly, which has a significant influence on the process of determining actuarial reserves. In this paper, conditional survival distributions of life insurance reserves are computed using copulas. Subsequently, the results are compared with an independence case. These calculations are based on selected Archimedean copulas and apply when the 'death of one individual' condition exists. The estimation outcome indicates that the insurer reserves calculated by means of Archimedean copulas are far more effective than those resulting from an independence assumption. The study demonstrates that copula-based dependency modelling improves the calculations of reserves made for actuarial purposes.

Modelling claims severity for obtaining insurance premium is one of the major concerns of the insurance industry. There is a considerable amount of literature on the actuarial application of the copula model to calculate the pure premium. In this paper, we model claims severity for computing the pure premium in the collision market by means of the count copula model. Moreover, we apply a regression model using a generalized beta distribution of the second kind (GB2) to compute the premium for an average claim and the conditional computation for all coverage levels. Like many other researchers, we assume that the number of accidents is independent from the size of claims. For real data application, we use a portfolio of a major automobile insurer in Iran in 2007-2008, with a subsample of 59,547 policies available in their portfolio. We then proceed to compare the estimated premiums with the real premiums. The results demonstrate that there is strong positive dependency between the real premium and the estimated one.

There are growing concerns for reserves estimation of incurred but not reported (IBNR) claims in actuarial sciences. In this paper, we propose a copula-based dependency model to capture the relationship between two main IBNR reserve variables, i.e., the "time between two successive occurrences" and "delay time".A maximum likelihood estimation method is used to estimate the parameters of the model. A simulation study is conducted to evaluate the validity of the theoretical results. Moreover, the proposed method is applied to predict the number of claims for the next years of a portfolio from a major automobile insurer and is compared to the classical CL model forecasting.

Introduction of the VgDGAT1A gene in soybean [Glycine max (L.) Merr.] genotypes increased both protein and oil content and resulted in earlier maturation compared with commonly cultivated soybean genotypes (i.e., Jack). However, the effect of VgDGAT1A gene on the length of the vegetative, reproductive, and the overall growth period of soybean has not been thoroughly evaluated. A randomized complete block design consisting of two transgenic soybean genotypes with VgD1-1 and VgD1-2 highly active acyl-CoA: diacylglycerol acyltransferase (DGAT) from ironweed [Vernonia galamensis (Cass) Less.] and nontransgenic control (Jack) was evaluated in field studies in 2015 and 2016 in Lexington, Kentucky. Levels of sucrose accumulation and seed weight were calculated for the three genotypes. Soybean grain yield, seed weight, and seed number were similar among all genotypes in both years. Modified genotypes reached the R7 (beginning of physiological maturity) stage earlier, and the rate of dry weight accumulation in individual seeds ranged between 2.8 to 4.4 mg seed −1 day −1 and was not different in comparison with the control (range: 3.4-4.7 mg seed −1 day −1 ). While days to reach R7 was shorter in VgD, there were no differences among genotypes for pod weight (PW), seed weight (SW), pod sucrose (PS), or seed sucrose (SS) concentrations. Linear plateau and cubic models were the best fit for seed weight for both years. These results indicated that despite earlier maturation in VgD genotypes, seed growth, and final soybean yield were similar among VgD and Jack.