In today’s world of financial uncertainty, one major public concern is to assess (and possibly improve) the stability of companies that take on risks. Actuaries have been aware of that issue for a very long time and have a great experience in modeling the activity of a risk business. During the first part of the twentieth century, they focused on the probability of ruin to assess the stability of their company. In his seminal paper of 1957 Bruno de Finetti criticized this approach and laid the foundations of what would become an increasingly popular topic: the study of dividend strategies. The contributions made by actuaries in that field constitute a substantial body of knowledge, whose interest is relevant not only to insurance but also to a much broader range of areas of practice. In this paper we aim at a taxonomical synthesis of the 50 years of actuarial research that followed de Finetti’s original paper.

Strategies for Dividend Distribution: A Review

In this paper we extend the results in Lin and Willmot (1999 Insurance: Mathematics and Economics 25, 63–84) to properties related to the joint and marginal moments of the time of ruin, the surplus before the time of ruin, and the deficit at the time of ruin. We use an approach developed in Lin and Willmot (1999) , under which the solution to a defective renewal equation is expressed in terms of a compound geometric tail, to derive explicitly the joint and marginal moments. This approach also allows for the establishment of recursive relations between these moments. Examples are given for the cases when the claim size distribution is exponential, combinations of exponentials and mixtures of Erlangs.

The moments of the time of ruin, the surplus before ruin, and the deficit at ruin

Modern industrial processes are characterized by acquiring massive amounts of highly collinear data. In this context, partial least-squares (PLS) regression, if wisely used, can become a strategic tool for process improvement and optimization. In this paper we illustrate the versatility of this technique through several real case studies that basically differ in the structure of the X matrix (process variables) and Y matrix (response parameters). By using the PLS approach, the results show that it is possible to build predictive models (soft sensors) for monitoring the performance of a wastewater treatment plant, to help in the diagnosis of a complex batch polymerization process, to develop an automatic classifier based on image data, or to assist in the empirical model building of a continuous polymerization process. Copyright © 2008 John Wiley & Sons, Ltd.

PLS: A versatile tool for industrial process improvement and optimization

This paper considers the stationary and the ordinary discrete renewal risk models. The main result is an expression of the Gerber–Shiu discounted penalty function in the stationary model in terms of the corresponding Gerber–Shiu function in the ordinary model. Subsequently, this relationship is considered in more detail in both the discount free case and under the compound binomial model. The latter case may be viewed as a discrete analog of the classical Poisson model. Simplifications of the general relationship are obtained, and a connection between the defective joint cumulative distribution functions of the surplus prior to ruin and the deficit at ruin in the stationary and the ordinary renewal risk models is established. Moreover, the defective probability function of the claim causing ruin is derived in the compound binomial case.

The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function

In this paper, we study ruin probabilities in two generalized risk models. The effects of timing of payments and interest on the ruin probabilities in the models are considered. The rates of interest are assumed to have a dependent autoregressive structure. Generalized Lundberg inequalities for the ruin probabilities are derived by a renewal recursive technique. An illustrative application is given to the compound binomial risk process.

Ruin probabilities with dependent rates of interest

The aggregate claims are modeled as a compound binomial process, and the individual claim amounts are integer-valued. We study f(x, y; u), the “discounted” probability of ruin for an initial surplus u, such that the surplus just before ruin is x and the deficit at ruin is y. This function can be used to calculate the expected present value of a penalty that is due at ruin, and, if it is interpreted as a probability generating function, to obtain certain information about the time of ruin. An explicit formula for f(x, y; 0) is derived. Then it is shown how f(x, y; u) can be expressed in terms of f(x, y; 0) and an auxiliary function h(u) that is the solution of a certain recursive equation and is independent of x and y. As an application, we use the asymptotic expansion of h(u) to obtain an asymptotic formula for f(x, y; u). In this model, certain results can be obtained more easily than in the compound Poisson model and provide additional insight. For the case u=0, expressions for the expected present value of a payment of 1 at ruin and the expected time of ruin (given that ruin occurs) are obtained. A discrete version of Dickson’s formula is provided.

Discounted probabilities and ruin theory in the compound binomial model

Upregulation of the TFEB-mediated lysosome function relieves 4-Hydroxynonenal-Induced apoptosis.

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Discounted probabilities and ruin theory in the compound binomial model

Upregulation of the TFEB-mediated lysosome function relieves 4-Hydroxynonenal-Induced apoptosis.