In this paper, the dependence structure of a Schur-constant model is investigated. A necessary and sufficient condition for a random vector to be Schur-constant is given, and some properties of the Schur-constant model are presented as well. Several applications of the Schur-constant model in...

In insurance mathematics, a compound Poisson model is often used to describe the aggregate claims of the surplus process. In this paper, we consider the dual of the compound Poisson model under a threshold dividend strategy. We derive a set of two integro-differential equations satisfied by the...

We study the possibility for international diversification of catastrophe risk by the insurance sector. Adopting the argument that large insurance losses may be a [`]globalizing factor' for the industry, we study the dependence of geographically distant insurance markets via equity returns. In...

In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by...

In this paper, we study the discrete-time renewal risk model with dependence between the claim amount random variable and the interclaim time random variable. We consider several dependence structures between the claim amount random variable and the interclaim time random variable. Recursive...

A catastrophe put option is valuable in the event that the underlying asset price is below the strike price; in addition, a specified catastrophic event must have happened and influenced the insured company. This paper analyzes the valuation of catastrophe put options under deterministic and...

We consider an optimal dividends problem with transaction costs where the reserves are modeled by a spectrally negative Lévy process. We make the connection with the classical de Finetti problem and show in particular that when the Lévy measure has a log-convex density, then an optimal...

Theorem 15 of Embrechts et al. [Embrechts, Paul, Höing, Andrea, Puccetti, Giovanni, 2005. Worst VaR scenarios. Insurance: Math. Econom. 37, 115-134] proves that comonotonicity gives rise to the on-average-most-adverse Value-at-Risk scenario for a function of dependent risks, when the...

This paper uses a multivariate normal inverse Gaussian model to develop closed-form pricing formulas for both geometric and arithmetic basket options. For geometric basket options, an exact analytical solution is possible; for arithmetic basket options, the formula is an approximation. The model...

In this article, we study two optimization problems. The first is finding the best L1-approximant of a given random vector on some affine subspaces subject to a measurability condition. The second is finding the optimal allocation of policy limits such that the expected retained loss is...