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 paper is concerned with singular stochastic control for non-degenerate problems. It generalizes the previous work in that the model equation is nonlinear and the cost function need not be convex. The associated dynamic programming equation takes the form of variational inequalities. By...

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...

The estimation of future loan losses is not only important for financial institutions to effectively control the credit risk of commercial loan portfolio, but also an essential component in the capital plan submitted for regulatory approval in the annual CCAR and DFAST stress testing. Under the...

The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter problem by duality in convex analysis. The dual to the control problem is to find the supremum of all smooth subsolutions to...