Maria de Lourdes Centeno

Measuring the effects of reinsurance by the adjustment coefficient in the Sparre Anderson model

We study the insurer’s adjustment coefficient as a function of retention levels for combinations of quota-share with excess of loss reinsurance in the Sparre Anderson (1957) model. We show that the insurer’s adjustment coefficient is a unimodal function of the retention levels when the quota-share reinsurance premium is calculated on original terms and when the excess of loss premium is calculated according to the expected value principle.

Optimal Reinsurance for Variance Related Premium Calculation Principles

This paper deals with numerical computation of the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk and the reinsurance loading is an increasing function of the variance. We compare the optimal treaty with the best stop loss policy. The optimal arrangement can provide a significant improvement in the adjustment coefficient when compared to the best stop loss treaty. Further, it is substantially more robust with respect to choice of the retention level than stop-loss treaties.

Excess of loss reinsurance and Gerber’s inequality in the Sparre Anderson model

Abstract Assuming that the reinsurance premium is calculated according to the expected value principle we study an upper bound for the probability of ruin in finite horizon, as function of the excess of loss retention limit. The upper bound used is an extension proved by Grandell [Aspects of Risk Theory, Springer, New York, 1991] of Gerber’s bound, see Gerber [Martingales in risk theory, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 1973, pp. 205–216], for the Sparre Anderson model [On the collective theory of risk in the case of contagious between the claims, in: Proceedings of the Transactions on XV International Congress of Actuaries, New York, 1957].

Bonus systems in an open portfolio

Abstract In this paper, we study bonus systems in an open portfolio, i.e. we consider that a policyholder can transfer his policy to a different insurance company at any time. We make use of inhomogeneous Markov chains to model the system and show, under reasonable assumptions, that the stationary distribution is independent of the market shares, and is easily calculated.

Excess of Loss Reinsurance and the Probability of Ruin in Finite Horizon

The upper bound provided by Lundbergs inequahty can be improved for the probablhty of rum in fimte horizon, as Gerber (1979) has shown This paper studies this upper bound as a functmon of the retention hmH, for an excess of loss arrangement, and compares it with the probability of ruin

Comparing Risk Adjusted Premiums from the Reinsurance Point of View

In this paper we compare, from the point of view of reinsurance, the several risk adjusted premium calculation principles considered in Wang (1996b). We conclude that, with the exception of the proportional hazard (PH) premium calculation principle, all the others behave in a way similar to the expected value principle. We prove that the stop loss reinsurance premium when calculated using the PH premium principle gives a higher premium than any of the other transforms, provided that the priority is big enough. We observe a similar behaviour with respect to excess of loss reinsurance in all the examples given. We also study the behaviour of the adjustment coefficient, both from the insurers and the reinsurers point of view as functions of the priority, when the PH principle is used as opposed to the expected value principle.

Optimal Bonus Scales Under Path-Dependent Bonus Rules

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.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.