M 394C (57720) Stochastic Processes I

Time: TTH 2:00 – 3:00 pm

Room: 11.176

Instructor: Thaleia Zariphopoulou

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

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

BACKGROUND: The course will build on material covered in Probability I (Fall 2012) and

Probability II (Spring 2013.) 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.

TEXTBOOKS: The following textbooks are recommended (not required):

1.     Stochastic Differential Equations (B. Oksendal- 6th edition)

2.     Controlled Markov Processes and Viscosity Solutions (W.H. Fleming and M. H. Soner- 2nd edition).

3.     Brownian motion and stochastic calculus (I. Karatzas and S. Shreve).

Class notes will be distributed.