8117: Topics in Advanced Microeconomics

Spring 2025

8117 Stochastic calculus and Dynamic Programing

Instructor: Aldo Rustichini

The course is an introduction to basic concepts of stochastic calculus and application in economic analysis and finance. The aim of the course is to provide a treatment of the prerequisites. The requirements are basic probability and real analysis concepts; these will be reviewed in the first lectures.

A. Introduction

A.1 Dynamic Programming in Continuous time

B. Basic probability Concepts

Section B.1. Prerequisites: sigma-field, measurable function, probability measure, Probability spaces

Section B.2. Stochastic processes, filtration, stopping times

Section B.3. Conditional expectation

Section B.4. Discrete time martingales

C. Stochastic Calculus              

Section C.1. Convergence of Random Variable

Section C.2. Brownian Motion

Section C.3. Ito's Integral

Section C.4. Stochastic Differential Equations and Ito's Lemma

D. Optimization with Diffusion processes

Section D.1 Value Function

Section D.2. HJB equation

Section D.3. Viscosity Solutions