The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding

Abstract If Vk is the discount factor for the kth period, then Z = Σ k⩾1V 1...Vk Ck is the discounted value of a perpetuity paying Ck at time k. In some cases Z is also the limiting distribution of St =Vt (St-1 +Ct-1 ). This paper 1. reviews the literature concerning Z and {St } 2. considers continuous-time counterparts of Z and S, at the same time deriving the distribution of ∫ exp(-γt-σWt )1(0, ∞) (t)dt when W is Brownian motion; 3. gives applications to risk theory and pension funding.

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