The evolution of prices in market is usually given by geometric Brownian motion, where the Brownian process describes fluctuations is often called "white" noise. We study the effect of correlations introduced by a "colored" noise. We demonstrate how the "color" Brownian process may capture the...

This volume was written in honor of Wendell H. Fleming, a mathematician who has made fundamental contributions in the fields of calculus of variations, geometric measure theory, differential games, stochastic control theory, and population genetics. This book includes authoritative expositions...

The stressed probability of default and rating migration are important for the banks to assess the adequacy of credit reserve and credit capital under the stress market condition. Credit reserves are designed to cover the expected loss which can be estimated by the through-the-cycle probability...