Characterizing activity-dependent processes with a piecewise exponential model

Exponential and Piecewise Exponential Distributions

Since lifetimes are almost always non-negative, the normal model/distribution may not be appropriate. An easy to use, positive distribution is the exponential distribution. To a less extend, exponential distributions to the survival analysis is like normal distributions to the linear model/ANOVA. Piecewise exponential distribution is also used to bridge/connect the parametric and nonparametric ...

A Simple Exponential Model for Dependent Defaults

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of multi-name credit derivatives and Collateralized Debt Obligations. In this paper we study a simple and tractable intensity-based model for correlated defaults, in which unpredictable default arrival times are jointly exponentially distributed. Si...

Piecewise Stationary Markov Decision Processes, II: State-Dependent Gain

An Exponential Model for Dependent Defaults

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of multi-name credit derivatives and Collateralized Debt Obligations. In this paper we study a simple and tractable intensity-based model for correlated defaults, in which unpredictable default arrival times are jointly exponentially distributed. Si...

Piecewise-linear Diffusion Processes

Diffusion processes are often regarded as among the more abstruse stochastic processes, but diffusion processes are actually relatively elementary, and thus are natural first candidates to consider in queueing applications. To help demonstrate the advantages of diffusion processes, we show that there is a large class of one-dimensional diffusion processes for which it is possible to give conven...