Junior Level Math and Probability for Finance Seminar
An informal, expository seminar on probability theory, stochastic calculus, and PDEs for Math Finance at a level accessible to senior math undergraduates. The primary goal of the seminar is for students to help each other narrow the gap between the probability curriculum and the tools necessary for a detailed study of financial mathematics. All participants are encouraged to give talks.
We will meet on a bi-weekly basis starting Wed Jun 20 in BA6180 at 3:00 pm.
If you would like to speak, or contribute to the list of possible future topics, contact 'firstname.lastname@example.org'.
- The Wednesday August 1 session has been cancelled as no one has volunteered to speak; if you are interested please consider presenting at the following session.
- To avoid spamming broader mailing lists with seminar info, we are trying to put together an email list of participants. If you would like information about upcoming sessions, please email 'email@example.com' with your contact information.
- Date TBA: The Feynman-Kac formula
- Introduction to the General Theory of Stochastic Integration (w.r.t. Semimartingales) - Wed July 18 - Dylan Butson
- Riemann-Stieltjes integral, the (deterministic) integral process, properties, intuition, lots of pictures, total variation, integrability criterion; Martingales, the general Ito integral for square-integrable martingales, quadratic variation, properties of integral process; semimartingales, sketched proof of Ito formula for non-continuous semimartingales. Note: Throughout only continuous integrands will be treated to avoid (for now) subtleties of predictability.File:SC Lecture Slides 1.pdf
- Introduction to Stochastic Integration - Wed July 4 - Anne Dranovski
- Picking up where the last talk left off, this talk will give an elementary introduction to the stochastic integral. Scope: Riemann-Stieltjes integral; Brownian Motion; Ito integral; Examples; Black-Scholes PDE, if time allows. File:Stoch calc.pdf
- Recap of Modern Probability Theory - Wed Jun 20 - Dylan Butson
- Measure spaces, integration and the monotone class theorems; probability spaces and random variables; real-valued random variables and the connection to our regrettable years in undergrad probability – CDFs as image measures and PDFs as their Radon-Nikodym derivatives; intuitive meaning of sigma algebras as information, sigma algebras generated by random variables, filtrations; conditional expectations, probabilities and densities. File:Summary Notes 1.pdf
Possible Subjects for Future Talks
- Introduction to continuous time martingales
- Existence theorems: Kolmogorov, Ionescu Tulcea, Brownian motion
- Integration with respect to Brownian motion, Ito diffusions, Ito's formula for diffusions
- General theory of stochastic integration with respect to semimartingales (perhaps to be done in several parts)
- Change of measure with applications: martingale measures, numeraire, and the fundamental theorem(s) of asset pricing
- Introduction to continuous time Markov processes
- Random measures and point processes