We reconsider the valuation of barrier options by means of binomial trees from a “forward looking” prospective rather than the more conventional “backward induction” one used by standard approaches. This reformulation allows us to write closed-form expressions for the value of European and American put barrier-options on a non-dividend-paying stock.

This paper considers the optimal dividend payment problem in piecewise-deterministic compound Poisson risk models. The objective is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in certain special cases of risk ...

This paper deals with optimal dividend payment problem in the general setup of a piecewise-deterministic compound Poisson risk model. The objective of an insurance business under consideration is to maximize the expected discounted dividend payout up to the time of ruin. Both restricted and unrestricted payment schemes are considered. In the case of restricted payment scheme, the value function...

In the Cramér-Lundberg model and its di usion approximation, it is a classical problem to nd the optimal dividend payment strategy that maximizes the expected value of the discounted dividend payments until ruin. One often raised disadvantage of this approach is the fact that such a strategy does not take the life time of the controlled process into account. In this paper we introduce a value f...

In this paper,we consider a general Lévy riskmodelwith two-sided jumps and a constant dividend barrier. We connect the ruin problem of the ex-dividend risk process with the first passage problem of the Lévy process reflected at its running maximum. We prove that if the positive jumps of the risk model form a compound Poisson process and the remaining part is a spectrally negative Lévy process w...

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

Consider two insurance companies (or two branches of the same company) that have the same claims and they divide premia in some specified proportions. We model the occurrence of claims according to a Poisson process. The ruin is achieved if the corresponding two-dimensional risk process first leave the positive quadrant. We consider different kinds of linear barriers. We will consider two scena...

In the classical Cramér-Lundberg model in risk theory the problem of maximizing the expected cumulated discounted dividend payments until ruin is a widely discussed topic. In the most general case within that framework it is proved (Gerber (1969), Azcue & Muler (2005), Schmidli (2007)) that the optimal dividend strategy is of band type. In the present paper we discuss this maximization problem ...

In this paper, we consider the dividend payments prior to absolute ruin in a Markovian regime-switching risk process in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying Markov jump process. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the n th moment of the disc...