Article1990

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

379 citations0/0 files storedScandinavian Actuarial Journal

No readable copy stored yet — this record is metadata only.

Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

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.

Citations in this library

Stored only when both papers are in the corpus — 379 citations exist upstream.

References

1976Stochastic Differential Equations: Theory and Applications.2006Stochastic Differential Equations 1972Stochastic Differential Equations 1979An introduction to mathematical risk theory 1966A New Representation for Stochastic Integrals and Equations 2007Stochastic Differential Equations: Theory and Applications

Cited by

2003A survey and some generalizations of Bessel processes 1998Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution 2005Exponential functionals of Lévy processes 2004Spectral Expansions for Asian (Average Price) Options 2005Exponential functionals of Brownian motion, I: Probability laws at fixed time 2000Some Notes on the Dynamics and Optimal Control of Stochastic Pension Fund Models in Continuous Time 1993Risk theory in a stochastic economic environment 2006PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

Imported from OpenAlex (CC0) — nothing here is generated.