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DTSTART:20070311T020000
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DTSTAMP:20250120T212804
DTSTART;TZID=America/Detroit:20250122T160000
DTEND;TZID=America/Detroit:20250122T170000
SUMMARY:Lecture / Discussion:Student Model Theory Seminar
DESCRIPTION:First meeting of the student model theory reading seminar. Please contact Dhruv (dhruvkul@umich.edu) if you have any questions.
UID:131491-21868624@events.umich.edu
URL:https://events.umich.edu/event/131491
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Graduate Students,Mathematics,seminar,Talk,Undergraduate Students
LOCATION:East Hall - 1060
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20250104T120928
DTSTART;TZID=America/Detroit:20250122T160000
DTEND;TZID=America/Detroit:20250122T170000
SUMMARY:Workshop / Seminar:Vector-valued robust stochastic control with applications to finance
DESCRIPTION:We study a dynamic stochastic control problem subject to Knightian uncertainty with multi-objective (vector-valued) criteria. Assuming the preferences across expected multi-loss vectors are represented by a given\, yet general\, preorder\, we address the model uncertainty by adopting a robust or minimax perspective\, minimizing expected loss across the worst-case model. In contrast to the scalar case\, major challenges for multi-loss control problems include properly defining and interpreting the notions of supremum and infimum\, and addressing the non-uniqueness of these suprema and infima. To deal with these\, we employ the notion of an ideal point vector-valued supremum for the robust part of the problem\, while we view the control part as a multi-objective (or vector) optimization problem. Using a set-valued framework\, we derive both a weak and strong version of the dynamic programming principle (DPP) or Bellman equations by taking the value function as the collection of all worst expected losses across all feasible actions. The weak version of Bellman's principle is proved under minimal assumptions. To establish a stronger version of DPP\, we introduce the rectangularity property with respect to a general preorder. We also further study a particular\, but important\, case of component-wise partial order of vectors\, for which we additionally derive DPP under a different set-valued notion for the value function\, the so-called upper image of the multi-objective problem. Finally\, we provide illustrative examples motivated by financial problems.
UID:129023-21862050@events.umich.edu
URL:https://events.umich.edu/event/129023
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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