In applications of collective risk theory, complete information for the distribution of individual claims amount is often unknown, but reliable estimates of its first few moments may be available. Dickson and Waters [Dickson, D.C.M. and Waters, H.R., (2004) Some optimal dividends problems, Astin...

The uncontrolled surplus of an insurance company is a classical risk model. Now the risk model includes three features, namely debit interest, short-term and long-term invested interest, and linear dividend barrier. In this paper, the PDMP method and martingales are used for solvency studies in...

In this paper, we consider the dual of the compound Poisson risk model with exponentially distributed observation time and constant dividend barrier strategy. We derive and solve the integro-differential equations satisfied by the expected total discounted dividend payments until ruin and ruin...

In order to model random population dynamics with cycles in ecosystems, we construct a diffusion process with random jumps from the boundary. The evolution of this new process is investigated. It is shown that the behavior of the whole process is uniquely determined by its first hitting time and...

Estimation for the Birnbaum-Saunders (BS) regression model has been discussed by various authors when data are either complete or subject to Type-I or random censoring. But, this problem has not been considered for the case of interval censoring. In this article, we discuss the estimation of a...