Showing papers in "Scandinavian Actuarial Journal in 2002"
TL;DR: In this paper, the authors analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism, and they specifically model the smoothing mechanism used by most Danish life insurance companies and pension funds.
Abstract: We analyze minimum rate of return guarantees for life-insurance (investment) contracts and pension plans with a smooth surplus distribution mechanism. We specifically model the smoothing mechanism used by most Danish life-insurance companies and pension funds. The annual distribution of bonus will be based on this smoothing mechanism after taking the minimum rate of return guarantee into account. In addition, based on the contribution method the customer will receive a final (non-negative) undistributed surplus when the contract matures. We consider two different methods that the company can use to collect payment for issuing these minimum rate of return guarantee contracts: the direct method where the company gets a fixed (percentage) fee of the customer's savings each year, e.g. 0.5% in Denmark, and the indirect method where the company gets a share of the distributed surplus. In both cases we analyze how to set the terms of the contract in order to have a fair contract between an individual customer an...
101 citations
TL;DR: In this paper, an expected utility approach is proposed to price insurance risks in a dynamic financial market setting. But this approach relies heavily on risk preferences and yields two reservation prices -one each for the underwriter and buyer of the contract.
Abstract: We introduce an expected utility approach to price insurance risks in a dynamic financial market setting. The valuation method is based on comparing the maximal expected utility functions with and without incorporating the insurance product, as in the classical principle of equivalent utility. The pricing mechanism relies heavily on risk preferences and yields two reservation prices - one each for the underwriter and buyer of the contract. The framework is rather general and applies to a number of applications that we extensively analyze.
98 citations
TL;DR: In this paper, the authors present an overview of the standard risk sharing model of insurance and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums.
Abstract: In this paper we present an overview of the standard risk sharing model of insurance We discuss and characterize a competitive equilibrium, Pareto optimality, and representative agent pricing, including its implications for insurance premiums We only touch upon the existence problem of a competitive equilibrium, primarily by presenting several examples Risk tolerance and aggregation is the subject of one section Risk adjustment of the probability measure is one topic, as well as the insurance version of the capital asset pricing model The competitive paradigm may be a little demanding in practice, so we alternatively present a game theoretic view of risk sharing, where solutions end up in the core Properly interpreted, this may give rise to a range of prices of each risk, often visualized in practice by an ask price and a bid price The nice aspect of this is that these price ranges can be explained by "first principles", not relying on transaction costs or other frictions We also include a short d
91 citations
TL;DR: In this paper, the authors consider the problem of finding optimal dynamic premium policies in non-life insurance, where the reserve of a company is modeled using the classical Cramer-Lundberg model with premium rates calculated via the expected value principle.
Abstract: In this paper we consider the problem of finding optimal dynamic premium policies in non-life insurance. The reserve of a company is modeled using the classical Cramer-Lundberg model with premium rates calculated via the expected value principle. The company controls dynamically the relative safety loading with the possibility of gaining or loosing customers. It distributes dividends according to a 'barrier strategy' and the objective of the company is to find an optimal premium policy and dividend barrier maximizing the expected total, discounted pay-out of dividends. In the case of exponential claim size distributions optimal controls are found on closed form, while for general claim size distributions a numerical scheme for approximations of the optimal control is derived. Based on the idea of De Vylder going back to the 1970s, the paper also investigates the possibilities of approximating the optimal control in the general case by using the closed form solution of an approximating problem with exponen...
60 citations
TL;DR: In this article, it was shown that vectors (S M 1, S Mn ) and (S' M'1, M n ) of random sums of positive random variables are stochastically ordered by upper orthant dependence, lower orthant dependency, concordance or by the supermodular ordering whenever their corresponding random numbers of terms (M 1, …, M n ), and (M' 1,...,..., M' n ) are themselves ordered in this fashion.
Abstract: It is shown that vectors ( S M 1 , … , S Mn ) and ( S' M'1 , …, S' M'n ) of random sums of positive random variables are stochastically ordered by upper orthant dependence, lower orthant dependence, concordance or by the supermodular ordering whenever their corresponding random numbers of terms ( M 1 , … , M n ) and ( M' 1 , … , M' n ) are themselves ordered in this fashion. Actuarial applications of these results are given to different dependence structures for the collective risk model with several classes of business.
46 citations
TL;DR: A fully Bayesian approach to non-life risk premium rating, based on hierarchical models with latent variables for both claim frequency and claim size, is proposed and it is shown that interaction among latent variables can improve predictions significantly.
Abstract: We propose a fully Bayesian approach to non-life risk premium rating, based on hierarchical models with latent variables for both claim frequency and claim size. Inference is based on the joint posterior distribution and is performed by Markov Chain Monte Carlo. Rather than plug-in point estimates of all unknown parameters, we take into account all sources of uncertainty simultaneously when the model is used to predict claims and estimate risk premiums. Several models are fitted to both a simulated dataset and a small portfolio regarding theft from cars. We show that interaction among latent variables can improve predictions significantly. We also investigate when interaction is not necessary. We compare our results with those obtained under a standard generalized linear model and show through numerical simulation that geographically located and spatially interacting latent variables can successfully compensate for missing covariates. However, when applied to the real portfolio data, the proposed models a...
37 citations
TL;DR: In this article, the authors apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model.
Abstract: This paper describes how to apply Markov Chain Monte Carlo (MCMC) techniques to a regime switching model of the stock price process to generate a sample from the joint posterior distribution of the parameters of the model. The MCMC output can be used to generate a sample from the predictive distribution of losses from equity linked contracts, assuming first an actuarial approach to risk management and secondly a financial economics approach. The predictive distribution is used to show the effect of parameter uncertainty on risk management calculations. We also explore model uncertainty by assuming a GARCH model in place of the regime switching model. The results indicate that the financial economics approach to risk management is substantially more robust to parameter uncertainty and model uncertainty than the actuarial approach.
36 citations
TL;DR: In this article, the authors consider the collective risk model for the insurance claims process and adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question.
Abstract: This paper considers the collective risk model for the insurance claims process. We will adopt a Bayesian point of view, where uncertainty concerning the specification of the prior distribution is a common question. The robust Bayesian approach uses a class of prior distributions which model uncertainty about the prior, instead of a single distribution. Relatively little research has dealt with robustness with respect to ratios of posterior expectations as occurs with the Esscher and Variance premium principles. Appropriate techniques are developed in this paper to solve this problem using the k -contamination class in the collective risk model.
14 citations
TL;DR: In this paper, two methods for approximating a given risk with the aid of the s-convex extremal distributions are proposed, and the goodness of these stochastic approximations is asserted using stop-loss distances.
Abstract: This paper aims to further investigate the structure of the s-convex stochastic extrema. The present study is based on a remarkable probabilistic generalization of Taylor’s theo- rem obtained by Lin (1994). Two methods for approximating a given risk with the aid of the s-convex extremal distributions are then proposed. The goodness of these stochastic approximations is asserted using stop-loss distances.
13 citations
TL;DR: In this paper, recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and compound mixed poisson distributions, in the case where th...
Abstract: Recursive formulae are derived for the evaluation of the moments and the descending factorial moments about a point n of mixed Poisson and compound mixed Poisson distributions, in the case where th...
10 citations
TL;DR: In this paper, a risk process where the claims are sums of dependent random variables is considered and the influence of the dependence on the infinite and finite-time Lundberg exponent is investigated and monotonicity results are obtained.
Abstract: A risk process where the claims are sums of dependent random variables is considered. Using the supermodular order the influence, the dependence has on the infinite- and finite-time Lundberg exponent is investigated and monotonicity results are obtained.
TL;DR: In this article, the authors considered an endowment insurance contract with a twelve months maturation time and derived upper and lower bounds of the premium, the death and survival benefits for a hetrogeneous population of insureds.
Abstract: In the paper we consider an endowment insurance contract with a twelve months maturation time. Using the majorization order and Schur-convex functions we derive upper and lower bounds of the premium, the death and survival benefits for a hetrogeneous population of insureds. The bounds are obtained for the exponential, Balducci, and linear approximations.
TL;DR: In this article, the authors deduced the optimal scales for bonus malus systems that are not first order Markovian processes, but that can be regarded as Markovians by increasing the number of states of the system.
Abstract: Bonus malus systems have been studied by several authors under the framework of Markov chains. Optimal scales have been deduced by Norberg (1976), Borgan, Hoem & Norberg (1981) and Gilde & Sundt (1989). In these articles the authors assumed that the bonus system forms a first order Markov chain. In the present paper we deduce the optimal scales, using the same criteria as in the cited papers, for bonus systems that are not first order Markovian processes, but that can be regarded as Markovian by increasing the number of states of the system.