Threshold dividend strategies for a Markov-additive risk model

Abstract

We consider the following risk reserve model. The premium income is a level dependent Markov-modulated Brownian motion. Claim sizes are iid with a phase-type distribution. The claim arrival process is a Markov-modulated Poisson process. For this model the payment of dividends under a threshold dividend strategy and the time until ruin will be analysed.

Implied liquidity: Model sensitivity

“…It is known that W (x) is non-singular for x > 0 and so is F (θ) in the domain of interest. In addition, (6) W…”

A Risk Model with an Observer in a Markov Environment

“…In principle, the matrix L can be obtained from W (x), cf. (6). This method, however, is ineffective and numerically unstable.…”

“…where the second equality follows from (6). Under assumption that all the eigenvalues of Λ andΛ are semi-simple (there are n eigenvectors in each case), this implies that M (x) converges to a finite limit U and ΛU − UΛ = L∆.…”

“…The proof of Theorem 4.1 relies on an approximation idea, which has already appeared in various papers, see e.g. [6,7,18]. We consider an approximation R (x) of the matrix R(x).…”