Course Announcement

Topics in Probability: Controlled Diffusion Processes, Math 8692, Spring 1997

Topics include

• Numerous examples of controlled diffusion processes including singular control problems arising in finance and problems with constraints like in finite fuel problem
• Connections with fully nonlinear elliptic and parabolic equations, in particular, elliptic and parabolic Monge-Ampère equations
• General properties of value functions (like Bellman's principle)
• Linear controlled processes with quadratic cost functions
• Existence and uniqueness of solutions of Bellman's equations
• -estimates of distribution densities of stochastic integrals
• Finding optimal and -optimal policies
• Viscosity solutions approach to stochastic control
• Numerical approximations of the solutions
• Controlled processes in domains

I do not know yet how far we will be able to go this quarter. In any case the idea is to continue the course next Fall if there is enough students interested in continuing.

Three homeworks will be assigned and will form part of the final grade.

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