**Professor **Patrick Cheridito

**Assistant **Michel Baes

**Time **Wed 3–5 pm (first meeting: Sep 20)

**Literature**
- F.T. Bruss (2000). Sum the odds to one and stop. Annals of Probability 28
- T.S. Ferguson (1989).
Who solved the secretary problem?
Statistical Science 4(3)
- T.S. Ferguson (2010).
Optimal Stopping and Applications
- D. Lamberton (2009).
Optimal Stopping and
American Options
- D. Lamberton and B. Lapeyre (2000). Introduction to Stochastic Calculus Applied to
Finance, Second Edition. Chapman and Hall/CRC, Boca Raton, Florida
- D.V. Lindley (1961). Dynamic programming and decision theory. J. Royal Stat. Society. Series C 10(1)
- F.A. Longstaff and E.S. Schwartz (2001)
Valuing American options by simulation: a simple least-squares approach.
Review of Financial Studies 14(1)
- G. Peskir and A. Shiryaev (2006). Optimal Stopping and Free-Boundary Problems. Lectures in Mathematics.
ETH Zurich

**Presentations**
- Sep 27

Definition of a stopping time in discrete time; essential supremum; Snell envelope in discrete finite time;
smallest supermartingale characterization; method of backwards induction; smallest optimal stopping time;
largest optimal stopping time; optional sampling theorem; Doob decomposition
- Oct 4

Snell envelope in discrete time for infinite time horizon; method of essential supremum; recursive relation;
existence and non-existence of optimal stopping rules; from finite to infinite horizon; ε-optimal
stopping times
- Oct 11

Markov sequences; regular conditional distribution; Markov kernel; shift operator; Chapman–Kolmogorov equations; strong Markov property; potential theory in discrete time
- Oct 18

Optimally stopping a Markov sequence; Wald–Bellman equation; superharmonic functions;
continuation/stopping set; iterative method
- Oct 25

Standard secretary problem; variants of the secretary problem; sum the odds to one and stop
- Nov 1

Stopping times in continuous time; Snell envelope; Doob–Meyer decomposition;
ε-optimal stopping times; regular processes; smallest optimal stopping time; largest optimal stopping time
- Nov 8

Continuous-time Markov processes; diffusion processes
- Nov 15

MLS functionals and related PDEs (or PIDEs)
- Nov 22

Free boundary problems; smooth fit and continuous fit
- Nov 29

Finding a solution by changing time/space/measure
- Dec 6

Optimally stopping the maximum of a process; nonlinear integral equations
- Dec 13

Sequential testing; change point detection
- Dec 20

American-style options

**
Reports **