Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options

Dan Pirjol and Lingjiong Zhu

Papers from arXiv.org

Abstract: The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of geometric Brownian motions with geometric stopping time, and the finite sum of the geometric Brownian motions. These results are extended to the discrete sum of the exponential L\'evy process. We derive tail asymptotics and compute numerically the asymptotic distribution function. We compare the results against the known results for the continuous time integral of the geometric Brownian motion up to an exponentially distributed time. The results are illustrated with numerical examples for life annuities with discrete payments, and Asian options.

Date: 2016-09
New Economics Papers: this item is included in nep-cmp, nep-rmg and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

Published in Insurance: Mathematics and Economics 2016, Volume 70, 19-37

Downloads: (external link)
http://arxiv.org/pdf/1609.07558 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1609.07558

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().