A bivariate Markov process comprises a pair of random processes which are jointly Markov. One of the two processes in that pair is observable while the other plays the role of an underlying process. We are interested in three classes of bivariate Markov processes. In the first and major class of interest, the underlying and observable processes are continuous-time with finite alphabet; in the s...

We explore sources of heterogeneity in rating migration behavior using a continuous time Markov chain. Working in continuous time circumvents of the embedding problem, allows for arbitrary prediction horizons, mitigates the censoring effect, and facilitates term structure modeling. By adopting a Bayesian estimation procedure we are able to estimate for each issuer profile its own continuous tim...

The theory of general state-space Markov chains can be strongly related to the case of discrete state-space by use of the notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated σ-algebras, though the minorization provided by the theory concerns small sets of order n and n-step tra...

The theory of general state-space Markov chains can be related strongly to the case of discrete state-space by use of Doeblin’s notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated -algebras, though the minorization provided by the theory concerns n-step transition kernels for s...

We examine project scheduling with net-present-value objective and exponential activity durations, using a continuous-time Markov decision chain. Based on a judicious partitioning of the state space, we achieve a significant performance improvement compared to the existing algorithms.

<p style='text-indent:20px;'>This paper investigates the pricing of European-style lookback options when price dynamics underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, appreciation rate and volatility depend on states economy described by continuous-time Markov chain process. We derive an exact, explicit closed-form solution for in two-s...