M 393C Stochastic Processes I  (54515)

 

Dr. Thaleia Zariphopoulou

MW 2 – 3pm

RLM 11.176

Course Description: 

In this class the following topics will be covered:

·      Part I

o   Ito integral and stochastic calculus

o   Stochastic Differential Equations (SDE)

o   SDE and linear partial differential equations

o   Applications to boundary value problems

o   Applications to optimal stopping

o   Introduction to filtering

·      Part II

o   Stochastic control of controlled diffusion processes

o   The Hamilton-Jacobi-Bellman equation

o   Viscosity solutions

o   Introduction to risk sensitive control

o   Introduction to singular stochastic control

o   Applications in Mathematical Finance and other areas will be also presented.

 

BACKGROUND: The course will build on material covered in Probability I and  Probability II.  While these courses are not prerequisites, familiarity with their content is strongly recommended. The students must have taken an advanced course of Real Analysis and/or Probability Theory.