RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper,we consider a kind of semi-Markov risk model(SMRM) with constant interest force and heavy-tailed claims,in which the claim rates and sizes are conditionally independent,both fluctuating according to the state of the risk business.First,we derive a matrix integro-diferential equation satisfied by the survival probabilities.Second,we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts.It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts,not on the state 1 with exponential claim sizes.