A Reinsurance Approach in a Two-Dimensional Model with Dependent Risks

We consider an insurer having two classes of insurance risks dependent through the number of claims of each risk in a given period of time. We assume that the insurer chooses a reinsurance strategy related to the first class of risk by means a proportional reinsurance contract; we also assume that the reinsurance strategy related to the second class of risk is of Excess of Loss reinsurance type. Within this paper, we study the possible optimal couples of proportional retention level and Excess of Loss retention limit

Dividends and Dynamic Solvency Insurance in Two-Dimensional Risk Models

In this paper we consider two-dimensional risk models where the claim counting processes of the two classes of business are assumed to be Poisson processes. We assume that the dividends are paid because of the presence of a reflecting upper barrier. Furthermore, in order to avoid ruin, we consider dynamic solvency insurance contracts that depend on two different definitions of time of ruin. We present a rather general model and, under different assumptions, we obtain the equations fulfilled by the discounted dividend payments and by the net single premium of dynamic solvency insurance. We also derive some boundary conditions and provide explicit solutions for some special cases

Thiele's differential equation generalized

A general model for the evaluation of insurance policies by means of the mathematical reserve is determined. We obtain an expression which allows us to draw generalized versions of the traditional Thiele\u2019s equation in di\ufb00erent stochastic hypothesis, both for the actualization and for the mortality intensity and, more in general, for the transition intensities. Mathematics Sub ject Classi\ufb01cations (2000). 91B28, 91B30, 91B7

Su un problema a doppia barriera

Under the assumption of an upper reflecting barrier, the net single premium of a dynamic solvency insurance contract is considered. Some properties are derived by means of integral and integral- differential equations. This premium is derived in a particular case. Furthermore, the dividends expected present value is considered and the equations fulfilled are derived with some properties

A Markov process interest and mortality model

For several years stochastic models have been proposed that are able to capture uncertainty linked to the future development both of \ufb01nancial and demographic components inherent in the policy. We consider a multistate life insurance contract and propose a model where both the interest intensity and the transition intensities, the latter describing the demographic structure, are managed by multistate stochastic models. In particular, we study a life insurance contract and derive di\ufb00erential equations of the mathematical prospective reserve. Finally, we study mean values of actualization factors and survival probabilities, and derive the di\ufb00erential equations they satisfy. Such results allow us to obtain adequate premium \ufb02ows. Mathematics Sub ject Classi\ufb01cations (2000). 60J27, 91B30, 91B7

Un confronto tra adjustment coefficient ed economic indexes of riskiness nell'ambito della teoria collettiva del rischio

Con riferimento al "modello a tempo discreto" della teoria collettiva del rischio, consideriamo alcune relazioni dell'Economic Index of Riskiness di Aumann-Serrano e dell'Operational Measure of Riskiness di Foster-Hart con l'Adjustment Coefficient. Da queste studiamo valori della ricchezza iniziale di una compagnia di assicurazione che le danno la certezza di una prefissata limitazione sulla probabilit\ue0 di rovina. Concludiamo con il caso della riassicurazione in quota