Probability and Statistics Seminar: Existence and Properties of Optimal Strategies for Distribution-Constrained Optimization Problems

Friday, December 2, 2022 at 3:30pm to 4:30pm

This is a past event.

Kaprielian Hall (KAP), 414
3620 South Vermont Avenue, Los Angeles, CA 90089


Uwe Schmock, TU Wien [in-person]

or

Zoom Meeting: https://usc.zoom.us/j/99256720443?pwd=bHBNVkxURmVkandzdlQzaTlMMVZLUT09
Meeting ID: 992 5672 0443
Passcode: 908129

Abstract: We consider stochastic optimization problems in discrete time under distributional constraints. These problems are motivated by actuarial science, in particular to treat unit-linked insurance products with guarantees. They can also serve as benchmark models to account for customer behaviour, when the treatment as American option is not appropriate. The basic mathematical set-up is an adapted stochastic process (interpreted as pay-outs) and (possibly randomized) stopping times to optimize the expected pay-out. The difference to classical optimal stopping problems is our constraint concerning the distribution of the stopping times or, more generally, the adapted random probability measures. For these distribution-constrained optimization problems we prove the existence of an optimal strategy; the basic assumptions are suitable moment conditions. In special cases, optimal strategies are identified explicitly. Time permitting, also a continuous-time variant will be discussed. (The main part of this talk is based on joint work with Christiane Elgert and Karin Hirhager.)

Event Type

Lecture / Talk / Workshop

Campus

University Park Campus

Department
Mathematics
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