 Premiums arrive a constant rate "c" > 0 from customers and claims arrive according to a Poisson process with intensity "λ" and are independent and identically distributed non-negative random variables with distribution "F" and mean "μ" (they form a compound Poisson process).So for an insurer who starts with initial surplus "x",
The central object of the model is to investigate the probability that the insurer's surplus level eventually falls below zero (making the firm bankrupt).This quantity, called the probability of ultimate ruin, is defined as
where the time of ruin is formula_3 with the convention that formula_4.