Continuous-time perpetuities and time reversal of diffusions

Constantinos Kardaras () and Scott Robertson ()
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Constantinos Kardaras: London School of Economics
Scott Robertson: Carnegie Mellon University

Finance and Stochastics, 2017, vol. 21, issue 1, No 2, 65-110

Abstract: Abstract We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markovian model. Two approaches are used to obtain the distribution. The first identifies a partial differential equation for the conditional cumulative distribution function of the perpetuity given the initial factor value, which under certain conditions ensures the existence of a density for the perpetuity. The second (and more general) approach, using techniques of time reversal, identifies the joint law as the stationary distribution of an ergodic multidimensional diffusion. This latter approach allows efficient use of Monte Carlo simulation, as the distribution is obtained by sampling a single path of the reversed process.

Keywords: Perpetuities; Time reversal; Ergodic diffusions; Monte Carlo simulation; 91G60; 91B30; 60J60; 60J70 (search for similar items in EconPapers)
JEL-codes: G12 G13 G22 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00780-016-0308-0

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