Peter Laurence's Lecture Notes

Syllabus for the course




Lecture 1, version 1/22/2001 A general introduction to instruments, valuation methods and qualitative features of free boundary




Lecture 2, version 1/31/2001 A review of self-financing strategies and equivalent martingale measure in multi-period discrete setting




Lecture 3, version 2/5/2001 American options in the discrete setting from the probabilistic point of view: Snell envelopes, supermartingales, sup of expectation of intrinsic value over paths; Doob decomposition and greatest optimal stopping time.




Lecture 4, version 2/12/2001 American options in the discrete setting from the probabilistic point of view, continued. Hedging an american option in a complete market.




Lecture 5, version 2/26/2001 The relation between the optimal stopping formulation and the strong variational inequalities and the weak variational inequalities.




Lecture 6, version 3/7/2001 The beginning of the regularity theory, especially in one dimension




Lecture 7, version 4/1/2001 More on the regularity in one dimension and a bit in general case




Lecture 8, version 4/10/2001 The penalized problem in the case of an option on a basket




Lecture 9, version 4/10/2001 The penalized problem continued and passage to the limit




Lecture 10A, version 4/18/2001 Qualitative properties of the exercise region




A "Gallery" for Free Boundaries of options on a basket of two stocks









For an exposition of the viscosity solution approach and its relation to dynamic programming see the Lectures by S. R. Varadhan on ``PDES and Finance''