Peter Laurence's Lecture Notes

Click below to download my lecture notes in postscript format:

Lecture 1 (corrected June 2000) Some useful background material on the notion of projection, as applied to conditiomal expectation, linear regression, closed convex sets.

Lecture 2 On the CAPM and Markowitz's mean variance efficient portfolios, version Jan 25

Lecture 3 Arbitrage Pricing in one period model

Synopsis of Ch1 of "Quantitative Modeling"

Lecture 4 & 5 Farkas's lemma , complete and incomplete markets, upper and lower price of contingent claim. extra material on pricing in incomplete market. .

Lecture 6 Lower bounds on contingent claims in one period incomplete markets

Lecture 7 A Synopsis of ch2 of "Quantitative Modeling". e More on incomplete one period model, and begin the general multi period case, following the treatment in Lamberton and Lapeyre.

Lecture 8 Passage to limit in Binomial model (version Wednesday Feb 9)

Lecture 9 Statement of Kuhn Tucker Theorem, used in sub& superrep approach

Lecture 10 Continuation of self-financing in discrete multiperiod model

Lecture 11 More on complete and incomplete in multiperiod . This week we will go over american options as discussed in Lamberton and Lapeyre. Please read p11-12 and 17-20. The stopping time theory applied to a simple two period tree example .

Lecture 12 The stopping time problem in simple example, sequel .

Lecture 13 Green's functions for the heat equation and their connection to Black Scholes.

Lecture 14 Stochastic Calculus:First time over, the engineering approach, one dimensional case

Lecture 15 Multidimensional stochastic calculus and HJM, March28.

Lecture 16 Here is some supplementary material on cap pricing. Basically, it gives additional details for the derivation of the cap pricing formula when using the initial discount curve as initial data.

Lecture 17 Here are some ``review and learn fun new stuff too'' problems. They concern the Ornstein Uhlenbeck and Vasicek processes

I am a Visiting member in the Division of Quantitative Finance at Courant, N.Y.U., where I collaborate with Marco Avellaneda . If you are interested in computational finance, I recommend the online materials on Jonathan Goodman's site: Goodman. And if you are interested in an Pde's and control theory to the online materials on Bob Kohn's web page : Kohn. I am also a Professor of Mathematics in the Faculty of Statistics and Department of Mathematics at the Universita` di Roma, "La Sapienza". My research interests are in applied mathematics, especially in partial differential equations and free boundary problems arising in option pricing theory and in magnetohydrodynamics.

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