Displaying similar documents to “Pricing bonds and CDS in the model with rating migration induced by a Cox process”

Defaultable bonds with an infinite number of Lévy factors

Jacek Jakubowski, Mariusz Niewęgłowski (2010)

Applicationes Mathematicae

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A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Lévy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and sufficient conditions (generalized HJM conditions) under which the market is arbitrage-free. Connections with consistency conditions are discussed.

Risk-sensitive average optimality in Markov decision processes

Karel Sladký (2018)

Kybernetika

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In this note attention is focused on finding policies optimizing risk-sensitive optimality criteria in Markov decision chains. To this end we assume that the total reward generated by the Markov process is evaluated by an exponential utility function with a given risk-sensitive coefficient. The ratio of the first two moments depends on the value of the risk-sensitive coefficient; if the risk-sensitive coefficient is equal to zero we speak on risk-neutral models. Observe that the first...

Intertwining of birth-and-death processes

Jan M. Swart (2011)

Kybernetika

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It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling between a general birth-and-death process and a process whose birth rates are the negatives of...

Loop-free Markov chains as determinantal point processes

Alexei Borodin (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We show that any loop-free Markov chain on a discrete space can be viewed as a determinantal point process. As an application, we prove central limit theorems for the number of particles in a window for renewal processes and Markov renewal processes with Bernoulli noise.