BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Continuous Time Perpetuities and the Time Reversal of Diffusions Robertson, Scott


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

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