The present value of a stochastic perpetuity and the Gamma distribution

✍ Scribed by Moshe Arye Milevsky

• Book ID: 104299609
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 373 KB
• Volume: 20
• Category: Article
• ISSN: 0167-6687
• DOI: 10.1016/s0167-6687(97)00013-9

✦ Synopsis

We derive the probability density function of the present value of a perpetuity subjected to a stochastic Wiener rate of interest and prove that its inverse is Gamma distributed. This result is useful for computing the initial endowment required to fund a perpetuity, in a real world stochastic environment, under a fixed probabilistic confidence level. The proof relies on well-known martingale results from the theory of stochastic calculus. A numerical example is provided with tables.