On retrospective insurance premium (original) (raw)

Pricing insurance contracts under Cumulative Prospect Theory

Insurance: Mathematics and Economics, 2012

The aim of this paper is to introduce a premium principle which relies on Cumulative Prospect Theory by Kahneman and Tversky. Some special cases of this premium principle have already been studied in the actuarial literature. In the paper, properties of this premium principle are examined.

The finite-time ruin probability with dependent insurance and financial risks

Journal of Applied Probability, 2011

Consider a discrete-time insurance risk model. Within period i, the net insurance loss is denoted by a real-valued random variable X i . The insurer makes both risk-free and risky investments, leading to an overall stochastic discount factor Y i from time i to time i − 1. Assume that (X i , Y i ), i ∈ N, form a sequence of independent and identically distributed random pairs following a common bivariate Farlie-Gumbel-Morgenstern distribution with marginal distribution functions F and G. When F is subexponential and G fulfills some constraints in order for the product convolution of F and G to be subexponential too, we derive a general asymptotic formula for the finite-time ruin probability. Then, for special cases in which F belongs to the Fréchet or Weibull maximum domain of attraction, we improve this general formula to be transparent.

Insurance policy value and Pareto-optimal retention in the hypothesis of rare loss events

1998

In the hypothesis of rare loss events, the general expression of the policy value has been determined as a functional of the "expected frequency / loss severity" function and of the retention function. Exponential disutility has been chosen after mathematical characterization of some of its economical aspects, where functional properties of quasiarithmetic averages have been used. By means of variational techniques, in the case of a risk neutral Insurer the Pareto-optimal retention function has been finally determined.

Risk Theory with the Gamma Process

ASTIN Bulletin, 1991

The aggregate claims process is modelled by a process with independent, stationary and nonnegative increments. Such a process is either compound Poisson or else a process with an infinite number of claims in each time interval, for example a gamma process. It is shown how classical risk theory, and in particular ruin theory, can be adapted to this model. A detailed analysis is given for the gamma process, for which tabulated values of the probability of ruin are provided.

Ruin probabilities in classical risk models with gamma claims

Scandinavian Actuarial Journal, 2017

In this paper we provide three equivalent expressions for ruin probabilities in a Cramér-Lundberg model with gamma distributed claims. The results are solutions of integro-differential equations, derived by means of (inverse) Laplace transforms. All the three formulas have infinite series forms, two involving Mittag-Leffler functions and the third one involving moments of the claims distribution. This last result applies to any other claim size distributions that exhibits finite moments.