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OPTIMAL STOPPING – Theory and Applications

Du Mardi 26 Mai 2015 à 9h00 au Mercredi 27 Mai 2015 à 17h00

"OPTIMAL STOPPING – Theory and Applications "

by Thomas Bruss, ULB
  •  26/27 of May
  • at UCL, Institut de statistique, 20, Voie du Roman Pays, 1348 Louvain-La-Neuve,
  • Room : c.115

Lecture I (Tuesday, 10-12h30)
1. Objectives of this course;
Interplay of strong-information models (mathematical finance) and weak hypotheses models; Basic ideas and principles of strategic modelization;
Warm-up examples: the two-numbers problem; secretary problem; extensions;

2. Independent sequences; odds-algorithm; proofs; stopping on a last success; buying and selling; odds-algorithm for unknown odds; medical ethical problems and optimal stopping

Lecture II (Tuesday, 14h30-17h)
3. Sequential analysis; stopping times; Wald's equation; martingales; stopped martingales;non-measurable optional-times and their interest; first- and last-hitting times;

4. Recursive approaches; house-selling problem; Moser's problem; Kruskaltype iterations;
The hidden potential of randomness (the television show problem) and conclusions.

Lecture III (Wednesday, 10-12h30)
5. Unknown number of options; 1/e-law of best choice and proof; optimal buying and selling re-visited; venture capital and no-recall investment; allocation problems; parking problems;

6. Full-information problems; Moser's problem; online-selection of monotone subsequences; further applications in finance.

Lecture IV (Wednesday, 14h30-17h)
7. Harder stopping problems; last-arrival problem; stoch. proc. with proportional increments; Pascal proc.; computability of thresholds; optimal stopping with mixed constraints.

8. Approximation by differential equations; partially open and open problems (Robbins' problem of optimal stopp.; the general no-infomation problem.)

Outlook further research.

Dernière mise à jour par EDT STAT-ACTU Mercredi 8 Avril 2015