Abstract
In this paper, we consider a Markov-modulated risk model in which the claim inter-arrivals, claim sizes and premiums are influenced by an external Markovian environment process. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations derived by Reinhard [Reinhard, J.M., 1984. On a class of semi-Markov risk models obtained as classical risk models in a Markovian environment. ASTIN Bull., 14, 23–43]. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the K n -family, n ∈ N + . Examples are given with claim sizes that have exponential, Erlang and a mixture of exponential distributions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
