Stochastic models for claims reserving in insurance business

Abstract

Insurance companies have to build a reserve for their future payments which is usually done by deterministic methods giving only a point estimate. In this paper two semi-stochastic methods are presented along with a more sophisticated hierarchical Bayesian model containing MCMC technique. These models allow us to determine quantiles and confidence intervals of the reserve which can be more reliable as just a point estimate. A sort of cross-validation technique is also used to test the models.

Experience rating and stochastic reserving in general insurance

“…A family of models with the idea that the chain ladder factors are bootstrapped directly is presented in [36]. Suppose that each subsequent cumulative claim has a multiplicative link to the previous one in accident year j through a random variable α j .…”

“…Eventually, the NAIC database is an example of the latter. The principle is similar to the one suggested in [36], however, instead of sampling from C 1,j+1 C 1,j , . .…”

“…The assumption is similar to [36], however, now the cumulative claims are driven recursively by a j random variables stemming from an unknown distribution, identically distributed across the run-off triangles.…”

Analysis of Stochastic Reserving Models By Means of NAIC Claims Data

“…A family of models with the idea that the chain ladder factors are bootstrapped directly is presented in Faluközy et al (2007).…”

“…The assumption is similar to the one above Faluközy et al (2007), however, now the cumulative claims are driven recursively by a j random variables stemming from an unknown distribution, identically distributed across the run-off triangles.…”