Continuous-time perpetuities and time reversal of diffusions
type: Item
instance of: scholarly article
title: Continuous-time perpetuities and time reversal of diffusions
zbMATH Open document ID: 1390.91303
author: Constantinos Kardaras
author: Scott Robertson
published in: Finance and Stochastics
publication date: 2017-01-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1411.7551
review text: The authors discuss the estimation of the joint distribution of a continuous-time perpetuity and some underlying factors governing the cash flow rate under an ergodic Markovian model. They consider two approaches to the problem, namely the partial differential equation approach and the time reversal approach. In the partial differential equation approach, the authors derive a partial differential equation for the conditional cumulative distribution of the perpertuity given the initial values of the factors. In the time reversal approach, they obtain the joint probability law as the stationary distribution of an ergodic multi-dimensional diffusion. Section 2 describes the problem. The main results including the partial differential equation for the cumulative distribution function and the joint probability law based on the time reversal diffusion are presented in Section 3. In Section 4, the authors present a numerical example for the time reversal approach based on Monte Carlo simulation.
reviewed by: Tak Kuen Siu
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 6674101
zbMATH Keywords: time reversal
zbMATH Keywords: perpetuities
zbMATH Keywords: ergodic diffusions
zbMATH Keywords: Monte Carlo simulation
MaRDI profile type: Publication
OpenAlex ID: W2181491881
Wikidata QID: Q59615534
arXiv ID: 1411.7551
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DOI: 10.1007/S00780-016-0308-0
DBLP publication ID: journals/fs/KardarasR17
description: scientific article