FinM 345/STAT 390 Stochastic Calculus
Autumn 2009
Mondays, 6:30-9:30PM, Kent 120, Chicago;
Mondays, 7:30-10:30 pm, UBS, Stamford;
Tuesdays, 7:30-10:30 am, Spring, Singapore

Visiting Professor Floyd B. Hanson (hanson at math dot uchicago dot edu)

30 November 2009



Course Outline (tentative)

(Comments: This will be a more applied course than in the past, starting from stochastic differentials and stochastic integrals, as in the regular calculus, except with basic probabilities, then building up to stochastic differential equations and their solutions, eventually leading to financial applications and some useful abstract notions in stochastic calculus.

Knowledge of basic probability is assumed, but you can review background preliminaries from online sources given below.)

  1. Introduction to Stochastic Diffusion and Jump Processes: Basic properties of Poisson and Wiener stochastic processes. Based on the calculus model, differential and incremental models are discussed. The continuous Wiener processes model the background or central part of of financial distributions, while the Poisson jump process models the extreme, long tail behavior of crashes and bubbles of financial distributions. ... 1-2 Lectures

  2. Stochastic Integration for Stochastic Differential Equations: While the stochastic differentials and increments are useful in developing stochastic models and numerically simulating solutions, stochastic integration is important for getting explicit solutions or more manageable forms. ... 1 Lecture

  3. Elementary Stochastic Differential Equations (SDEs): The stochastic chain rules for jump-diffusions with simple Poisson jump processes, starting from diffusion chain rules to jump chain rules to jump-diffusion chain rules. Time-varying coefficients are also considered. ... 2 Lectures

  4. Stochastic Differential Equations for General Jump-Diffusions: Stochastic differential equations with compound Poisson processes, i.e., including randomly distributed jump-amplitudes, state-time dependent coefficients, multi-dimensional SDEs, Martingales and finite rate Levy jump-diffusion formulations. ... 2-3 Lectures

  5. Applications to Financial Engineering: Generalized Black-Scholes-Merton option pricing analysis, option pricing for jump-diffusions and stochastic volatility, using risk-neutral measures; also the important event Greenspan process. Of course, financial models and motivations will be used throughout the course. ... 1-2 Lectures

  6. Time Series Introduction and the relationship to SDE models: Time series models such as the discrete AR (autoregressive), MA (moving average), ARMA (combined), and ARCH (conditional "volatility") models, as time allows. ... 1-2 Lectures

Prerequisite Knowledge:


Some Related Resources of the Instructor and Prior FinM 345:


Web Source: http://www.math.uchicago.edu/~hanson/finm345a09.html

Email Comments or Questions to fhanson at math dot uchicago dot edu )