Brief description:

The course will offer an introduction to several aspects of stochastic analysis for Markov processes.  Among other topics to be covered are martingale theory, stochastic integration and stochastic calculus.  Emphasis will be given on the connection of the stochastic analysis to the theory of partial differential equations, in particular for the case of Markov diffusion processes.  An introduction to Stochastic Control will be also offered as well as applications to optimization models of asset pricing in economics, insurance and finance.

• Martingale Theory
• Brownian Motion
• Stochastic Integration
• Stochastic Calculus
• Feynman-Kac formula
• Stochastic Control of Markov Diffusion Processes
• The Hamilton-Jacobi-Bellman equation
• Singular Stochastic Control
• Stochastic Differential games
• Applications to Asset pricing: utility maximization, derivative pricing and equilibrium theory

Textbook:   (Recommended)

• I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus,Springer-Verlag, 1991.
• W. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer-Verlag, 1993.

E-mail address: zariphop@math.utexas.edu