Suppose that risk reserves of an insurance company are governed by a Markov-modulated classical risk model with parameters modulated by a finite-state irreducible Markov chain. The main purpose of this paper is to calculate ultimate ruin probability that ruin time, the first time when risk...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance...

Let ξ1,ξ2,… be an iid sequence with negative mean. The (m,n)-segment is the subsequence ξm+1,…,ξn and its score is given by max{∑m+1nξi,0}. Let Rn be the largest score of any segment ending at time n, Rn∗ the largest score of any segment in the sequence ξ1,…,ξn, and Ox the...

Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro–differential equations that are solved numerically for the three...