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stack exchange the rate an insurance company charges its policy holders alternates between r1 and r0. a new policy holder is initially charged at a rate r1 per unit of time. when a policyholder paying at a rate r1 has made no claims for the most recent s time units, then the rate harged becomes r0 per unit of time. the rate charged remains r0 until a claim is made, at which time it reverts back to r1. suppose that a given policyholer lives forever and makes claims at times according to poisson process with rate lambda.
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