Date | 2023-03-09 |
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Speaker | Stephan Sturm |

Dept. | Worcester Polytechnic Institute |

Room | 129-301 |

Time | 13:00-14:00 |

We revisit the question of the optimal time of an asset sale from the point of view of Sharpe's "Distribution Builder" approach: Instead of assuming the investor's risk preferences in form of a utility function, the investor provides themself a distribution that should be attained when selling the asset at a stopping time (specified a priori). This obviously begs the question of which distributions are attainable for an investor. We connect this problem to the Skorokhod embedding problem for one-dimensional diffusions and provide explicit representation for optimal stopping times as well as their expected values. In the case that the target distribution is specified from a parametrized family (e.g., log-normal distributions), we show that optimality involves a mean-variance trade-off similar to the efficient frontier in Markowitz's approach to portfolio optimization. This is joint work with Peter Carr.

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