FDM-Seminar: Isaac M. Sonin
Optimal Stopping of Markov Chains, Gittins Index and Related Optimization Problems
| What |
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| When |
Feb 17, 2012 from 11:15 AM to 01:00 PM |
| Where | Eckerstr. 1, room 404 |
| Contact Name | Kristin Ohneberg |
| Contact Phone | +49 761 203-7701 |
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FDM-Seminar: Isaac M. Sonin
Dept. of Mathematics, UNC at Charlotte, USA
"Optimal Stopping of Markov Chains, Gittins Index and Related Optimization Problems"
Abstract:
In this talk I will discuss the problem of Optimal Stopping (OS) of Markov Chains (MCs), the methods for its solution, the classical and the generalized Gittins indices and related problems: the Katehakis-Veinott Restart Problem and the Whittle family of Retirement Problems. The celebrated Gittins index, its generalizations and related techniques play an important role in applied probability models, resource allocation problems, optimal portfolio management problems as well as other problems of financial mathematics. It is well known that a connection exists between the Ratio (cycle) maximization problem, the Katehakis-Veinott (KV) Restart Problem and the Whittle family of Retirement Problems, and that their key characteristics, the classical Gittins index, the KV index, and the Whittle index are equal in a classical setting.
These indices were generalized by the author (Statistics and Probability Letters, 2008) in such a way that it is possible to use the so called State Elimination algorithm, developed earlier to solve the OS of MCs problem to calculate this common index. One of the goals of this talk is to demonstrate also that the equality of these indices is a special case of a similar equality for three simple abstract optimization problems. A more general - continue, quit, restart problem will be also discussed.