Abstract: In this paper we consider the Gerber-Shiu penalty function in the compound binomial risk model with time-correlated claims. It is assumed that each main claim will induce a by-claim but the occurrence of the by-claim may be delayed with a certain probability. Formulas for the probability generating function of the penalty function are obtained, together with the expression for the pen...

In this paper, we study the discounted free Gerber-Shiu function for the compound binomial risk model with by-claims and randomized dividend policy. Specifically, explicit expression for the discounted free Gerber-Shiu function is obtained. This result allows us to derive formulae for some useful insurance quantities, including the ruin probability, the probability function of the deficit at ru...

The aim of this work is to use a duality approach to study the pricing of derivatives depending on two stocks driven by a bidimensional Lévy process. The main idea is to apply Girsanov’s Theorem for Lévy processes, in order to reduce the posed problem to a problem with one Lévy driven stock in an auxiliary market, baptized as “dual market”. In this way, we extend the results obtained by Gerber ...

Closed solutions to the problem of pricing a Russian option when the stock is modeled by a diffusion with negative jumps are obtained. The Russian option is a perpetual American option on the maximum value of the stock. That stock is assumed to have the form of a Wiener process with drift and negative mixed–exponentially distributed jumps driven by a Poisson process. This result generalizes tho...

The Gerber method is used worldwide as a simple and rapid method for determining fat in raw and processed milks. However, the volume of the test portion used in the method has not been internationally agreed upon. A collaborative study was conducted to evaluate performance of the Gerber method using either a weighed test portion (11.13 g) or by a 10.77 mL test portion delivered by pipet. For ea...

The Satisfactory Partition problem consists in deciding if a given graph has a partition of its vertex set into two nonempty sets V1, V2 such that for each vertex v, if v ∈ Vi then dVi(v) ≥ s(v), where s(v) ≤ d(v) is a given integer-valued function. This problem was introduced by Gerber and Kobler [EJOR 125 (2000), 283–291] for s = ⌈ d 2 ⌉. In this paper we study the complexity of this problem ...

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where ...

Professors Hwang, Chang and Wu are to be congratulated for this interesting paper. The authors study ex ante insurance guaranty schemes. In particular, capital forbearance mechanism and stochastic interest rate are incorporated in their model, and an explicit formula for the risk-based premium of the insurance guaranty fund is derived. I am especially interested in Section 2.3 and Appendix A. I...