## Talks

Robustness of Affine Short Rate Models. Applying global sensitivity analysis to bond prices implied by Vasicek and CIR models gives insights into the sensitivity of each model.

## Primers/Puzzles

I sometimes decide I don't fully understand some area of mathematics I'm interested in and attempt to write the results and proofs clearly and carefully. Other times I stumble upon an interesting question and attempt to solve it. I find this helps me realize how well I comprehend the ideas, and serves as a good primer for when I return to the subject. I'm posting some of them below, but they are always works in progress. Hopefully, others may find them useful, too!

Modes of Convergence in Probability Theory. Proving the hierarchy of modes of convergence found in probability and measure theory.

Understanding the Market Price of Risk. I attempt to demystify the market price of risk appearing when pricing derivatives on non-tradable underlyings.

Solving the Black-Scholes PDE the Right Way. I show what I believe is a much more straightforward and standard approach to solving constant-coefficient advection-diffusion PDEs, of which the Black-Scholes PDE may be written. This is an alternative to the awkward change of variables needed and the transformation to the heat equation often found in financial texts (like Wilmott's Mathematics of Financial Derivatives, to pick on one).

Plane Passengers Arriving Consecutively. Given an airplane with 25 rows of 3/2 seating, I compute the probability of all 3 passengers assigned to a row on the side with 3 seats arriving consecutively, one after the other.

Markov Chains and Stationary Distributions. Why does any initial distribution converge to the stationary distribution in Markov chains? I hash out the properties needed of the transition matrix to ensure this important property for finite-state Markov chains.

## FCM Resources

A short Fortran code demonstrating how to write numerical data to a file for plotting.

I'll be putting together this list of resources I found helpful when taking FCM and studying for the quals. I'll add more resources as I remember which ones I liked, and as I hear topics that students are having trouble with.

## Fortran Resources

Here are a couple examples of reading two-dimensional data from a file into Fortran arrays.