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Mathematical Finance and Probability Seminars

Infinite sums of the geometric Brownian motion and generalizations

Tuesday, February 07, 2017 at 11:45am - 12:45pm

Dan Pirjol, JP Morgan:  The infinite sum of a geometric Brownian motion (gBM) sampled on a sequence of uniformly spaced times appears in problems of actuarial science and theoretical probability. For example this appears when considering the present value of a perpetuity: a fixed recurring payment made in perpetuity from an initial deposit of stock, assumed to follow a geometric Brownian motion. The talk studies the distributional properties of the infinite sum of the gBM. This can be characterized as the stationary distribution of a linear stochastic recursion. Tail asymptotics are derived, and the distribution is found numerically by solving an integral equation. Similar results are obtained for the sum of the gBM with a geometrically distributed stopping time. The results can be generalized further by replacing the gBM with an exponential Levy process.
Location   Hill 705

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Mathematical Finance Master's Program

Department of Mathematics, Hill 348
Hill Center for Mathematical Sciences
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