**Friday 8 November @ 4pm London time.**

In the sixth talk of our Ergodicity Economics seminar series, **James Holehouse** (Santa Fe Institute) will present his research on first-passage problems:

**First-Passage Time Distributions in One-Dimensional Ruin Problems**

In many cases, the distribution of the time to reach ruin is not adequately captured by the mean and variance of the first-passage time. Therefore, a complete understanding of the statistics behind a ruin problem requires examining the full probability distribution. In this presentation, James offers a solution for the first-passage time distribution on a generalized one-dimensional finite interval using the “backward” master equations approach and generating functions. He highlights several non-intuitive aspects of the ruin problem: (I) Ruin on disordered intervals cannot be effectively studied through simulations, (II) there is a highly variable spatial dependence of the first-passage time, and (III) the distributions of first-passage times appear as bimodal.

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