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Continuous Time Perpetuities and the Time Reversal of Diffusions

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we consider the problem of obtaining the\r\ndistribution of a continuous time perpetuity, where the non-discounted\r\ncash flow rate is determined by an ergodic diffusion. Using results\r\nregarding the time reversal of diffusions, we identify the distribution of\r\nthe perpetuity with the invariant measure associated to a certain\r\n(different) ergodic diffusion. This enables efficient estimation of the\r\ndistribution via simulation and, in certain instances, an explicit formula\r\nfor the distribution. Time permitting, we will talk about how Large\r\nDeviations Principles and results concerning Couplings of diffusions can\r\nbe used to estimate rates of convergence, thus providing upper bounds for\r\nhow long simulations must be run when obtaining the distribution.\r\n

Mathematics; Game theory, economics, social and behavioral sciences; Probability theory and stochastic processes; Mathematical finance

video/mp4

Author affiliation: Carnegie Mellon University

2014-10-29

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/50930

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/