syllabus (1) - Partial Dierential Equations for Finance...

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Partial Differential Equations for Finance G63.2706, Spring 2011 Mondays 5:10-7pm WWH 517 Instructor: Robert V. Kohn. Office: 502 WWH. Phone: 212-998-3217. Email: [email protected] Web: www.math.nyu.edu/faculty/kohn. Office hours: Mon 2-3 and Wed 5-6. Grader: Mert Gurbuzbalaban. Office: 425 WWH. Phone: 212-998-3227. Email: [email protected] Office hours: Tues 7-8pm. Special Dates: First lecture 1/24. No lecture 2/21 (Presidents’ Day) and 3/14 (Spring Break). The final exam will be 5/9 (the last class day, rather than exam period). Peter Carr will give a guest lecture (tentatively 3/7). Content: An introduction to those aspects of partial differential equations and optimal control most relevant to finance. PDE’s naturally associated to diffusion processes: the forward and backward Kolmogorov equations and their applications. Linear parabolic equations: fundamental solution, boundary value problems, maximum principle. Dynamic programming and optimal con- trol: Hamilton-Jacobi-Bellman equation, verification arguments, optimal stopping. Applications
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