On combining quota-share and excess of loss

This paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions.info:eu-repo/semantics/publishedVersio

Dependent risks and excess of loss reinsurance

In this paper we study, from the insurance point of view, the optimal excess of loss retention limits for two dependent risks. We consider two optimization criteria, which are quite connected. The expected utility of wealth with respect to the exponential utility function and the adjustment coefficient of the retained aggregate claims amount. We consider that the number of claims is generated by a bivariate Poisson distribution. The premium calculation principle used for the excess of loss treaties is the expected value principle. Although the systems of equations, that give the optimal solution for both problems, look quite similar, we will see that the optimal solution is heavily dependent on the criterion chosen.info:eu-repo/semantics/publishedVersio

The effect of the retention limit on the risk reserve

This paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions.info:eu-repo/semantics/publishedVersio

Comparison Between Shakespeare\u27s \u3cem\u3eRichard III\u3c/em\u3e and the Historical Richard III

The end and aim of the writer of this thesis is to make a study of Shakespeare\u27s Richard III as well as the historical Richard III. The point at issue is to see wherein and how far Shakespeare has disregarded historical facts and personages. In order to carry out a work of this nature it is necessary to make a thorough study and analysis of the vast drama that completes a series of historical plays written by the Bard of Avon . It is not only necessary to have a thorough understanding of the play but 1a also expedient to become acquainted with men who have devoted time and labor to give us the facts in the private life of Richard III. It is not less important to spend some time in going back to the fifteenth century England to get a birdseye view of the turbulent waves of the Civil War that swept the country during that period. The author of the paper will place special emphasis on the major discrepancies found in Shakespeare\u27s Richard III. A chapter will be devoted to the analysis of the play. A second chapter will picture Richard III as represented by Shakespeare, while another will set forth the reasons of the dramatic genius for the treatment of the unique Richard III. The historical Richard will be given ample consideration in the working out of this thesis

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 model [In: Transactions of the XV International Congress of Actuaries]. 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.info:eu-repo/semantics/publishedVersio

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

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].info:eu-repo/semantics/publishedVersio

Optimal per claim reinsurance for dependent risks

This paper generalizes the results on optimal reinsurance pre sented in Centeno and Guerra (2008) to the case of an insurer holding a portfolio of k dependent risks. It is assumed that the number of claims of a risk may depend on the number of claims of the other risks of the portfolio. Our aim is to determine the optimal form of reinsurance for each risk when the cedent seeks to maximize the adjustment coefficient of the retained portfolio - which is equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion - and restricts the reinsurance strategies to functions of the individual claims. Assuming that the premium calculation principle is a convex functional we prove existence and uniqueness of solutions and provide a necessary optimality condition. These results are used to find the optimal reinsurance policy for a given risk when the reinsurance loading is either proportional to the expected value or increasing with the variance of the ceded claims. The type of the optimal arrangement for a given risk only depends on the premium of that particular risk.info:eu-repo/semantics/publishedVersio

Optimal trading under coherent comonotonic risk measures

This paper deals with the optimal risk trading from the point of view of an individual who rates his position using a coherent comonotonic risk measure, assuming that the market price is also coherent and comonotonic. We obtain a simple and intuitive explicit solution in terms of Kusuoka representationinfo:eu-repo/semantics/acceptedVersio

Are quantile risk measures suitable for risk-transfer decisions?

Although controversial from the theoretical point of view, quantile risk measures are widely used by institutions and regulators. In this paper, we use a unified approach to find the optimal treaties for an agent who seeks to minimize one of these measures, assuming premium calculation principles of various types. We show that the use of measures like Value at Risk or Conditional Tail Expectation as optimization criteria for insurance or reinsurance leads to treaties that are not enforceable and/or are clearly bad for the cedent. We argue that this is one further argument against the use of quantile risk measures, at least for the purpose of risk-transfer decisions.info:eu-repo/semantics/publishedVersio

The optimal reinsurance strategy : the individual claim case

This paper is concerned with the optimal form of reinsurance when the cedent seeks to maximize the adjustment coefficient of the retained risk (related to the probability of ultimate ruin) – which we prove to be equivalent to maximizing the expected utility of wealth, with respect to an exponential utility with a certain coefficient of risk aversion – and restricts the reinsurance strategies to functions of the individual claims, which is the case for most nonproportional treaties placed in the market. Assuming that the premium calculation principle is a convex functional we prove the existence and uniqueness of solutions and provide a necessary optimality condition (via needle-like perturbations, widely known in optimal control). These results are used to find the optimal reinsurance policy when the reinsurance loading is increasing with the variance. The optimal contract is described by a nonlinear function, of a similar form than in the aggregate case.info:eu-repo/semantics/publishedVersio