Introduction to Continuous Time Finance

This course is an introduction to tools and theories of continuous-time finance. The course starts by covering the basic mathematical toolkit: stochastic processes in continuous-time, stochastic integration/differential equations, Ito’s lemma, connections to partial differential equations, etc. This is the most difficult part of the course and will require some digging through some more advanced mathematical/probability material, but it is really mostly an application of advanced undergraduate calculus combined with calculus based probability. It is good to have your old multivariate calculus textbook around. We are approaching this material from a user’s perspective, and not from a formal mathematics perspective—thus more derivations and fewer “proofs.” Given this background, we will then cover the main pricing tools: arbitrage and equilibrium pricing in continuous-time asset markets, with a focus on both the mechanics and intuition.