Showing papers in "Scandinavian Actuarial Journal in 1993"
TL;DR: In this paper, the authors consider an insurance model where the underlying point process is a Cox process and use a martingale approach, applied to piecewise-deterministic Markov processes, to obtain finite-time Lundberg inequalities.
Abstract: We consider an insurance model, where the underlying point process is a Cox process. Using a martingale approach, applied to piecewise-deterministic Markov processes, finite-time Lundberg inequalities are obtained.
44 citations
TL;DR: In this paper, a large deviation approach is used to obtain upper and lower bounds for the corresponding ruin probabilities, expressed in terms of the entropy function of the claims distribution, and a risk process with premiums depending on the current reserve is considered.
Abstract: A risk process with premiums depending on the current reserve is considered. A large deviation approach is used to obtain upper and lower bounds for the corresponding ruin probabilities. They are expressed in terms of the entropy function of the claims distribution
29 citations
TL;DR: In this article, the statewise reserve of a life insurance policy is viewed as a stochastic differential equation in a point process set-up, and the traditional Markov model and a more general semi-Markov model are considered.
Abstract: Thiele's differential equation for the statewise reserves of a life insurance policy is viewed as a stochastic differential equation in a point process set-up. Special attention is given to the traditional Markov model and to a more general semi-Markov model. Finally, a numerical example with qualifying period for disabled lives is considered.
23 citations
TL;DR: In this paper, it is shown that other recursions can be derived starting with claim number distributions from the class of modified power series distributions which also incorporates generalized Poisson, generalized negative binomial and the ones mentioned above.
Abstract: Distributions like Poisson, binomial, negative binomial or logarithmic behave well as claim number distribution in collective models. Besides, using these claim number distributions, the total claim probabilities can easily be evaluated recursively with the so-called Panjer recursion. This note shows that other recursions can be derived starting with claim number distributions from the class of modified power series distributions which also incorporates generalized Poisson, generalized negative binomial and the ones mentioned above. In addition it is shown that Panjer's recursion can be derived as a special case.
20 citations
Journal Article•
TL;DR: In this article, the integration by parts rule is applied to life insurance, utilizing the counting process nature of the development of the policy, the rule induces three classes of identities, some generalizing certain classical relationships between life annuities and assurances and some not hitherto encountered in the literature.
Abstract: The rule of integration by parts produces useful formulas for the present value of a payment stream. Applied to life insurance, utilizing the counting process nature of the development of the policy, the rule induces three classes of identities, some generalizing certain classical relationships between life annuities and assurances and some not hitherto encountered in the literature.
9 citations
TL;DR: In this paper, a non-stationary generalization of renewal reward processes is constructed using the ideas of renewal theory and moments and distributions of work life pension benefits are studied as sojourn time problems associated with these processes.
Abstract: Using the ideas of renewal theory, certain non-stationary generalizations of renewal reward processes are constructed. Moments and distributions of work life pension benefits are then studied as sojourn time problems associated with these processes. An application to the U.S. private pension system is also discussed, involving the measurement of the impact of vesting rules on the distribution of work life pension benefits.
3 citations