Chatterjee (2015) Modeling credit risk

This is a concise paper describing the Vasicek model. It serves the purpose of describing how banks should evaluate risk on loan assets, and provides a connection between the Black-Scholes option pricing model to pricing bonds or loans. [more]

Owen (1980) A table of normal integrals

This is an artcle of my recent acquaintance. It is about various integrals involving the standard normal distribution \(\Phi(x)\) and its derivative. Besides it is a handy reference, it is interesting to see how the author organize the hundreds of integrals in a manner that is easy to lookup. [more]

A rough description of Radon-Nikodym derivative

Radon-Nikodym theorem suggests, in simplified terms, that if we have two measures \(\mu,\lambda\) of the same space with \(\mu\) absolutely continuous with respect to \(\lambda\) and a function \(\phi\) is \(\mu\)-integrable, then \(\int_A \phi d\mu = \int_A \phi \frac{d\mu}{d\lambda} d\lambda\) which the term \(d\mu/d\lambda\) is called the Radon-Nikodym derivative. [more]

Martingale and local martingale

Martingale is a stochastic process with the martingale property. If we have \(X_t\) as the stochastic process, the martingale property says that \(\mathbf{E}[X_t\mid\mathcal{F}_s] = X_s\), for \(s\lt t\). Closely related to this is the local martingale. However, the Wikipedia page does not have it clearly explained. Here is my narrative.... [more]