Occupation densities in solving exit problems for Markov additive processes and their reflections

By Jevgenijs Ivanovs, Zbigniew Palmowski. 2011

79 citations recorded by the source corpus.

Abstract This paper solves exit problems for spectrally negative Markov additive processes and their reflections. So-called scale matrix, which is a generalization of the scale function of a spectrally negative Levy process, plays the central role in the study of the exit problems. Existence of the scale matrix was shown by Kyprianou and Palmowski (2008) [32, Thm. 3] . We provide the probabilistic construction of the scale matrix, and identify its transform. In addition, we generalize to the MAP setting the relation between the scale function and the excursion (height) measure. The main technique is based on the occupation density formula and even in the context of fluctuations of spectrally negative Levy processes this idea seems to be new. Our representation of the scale matrix W ( x ) = e − Λ x L ( x ) in terms of nice probabilistic objects opens up possibilities for further investigation of its properties.

Subfields: Management Information Systems, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/213f8bafcc0332138a10913814c3076a677d8e60

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In Management Information Systems

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Optimal dividends in the dual model under transaction costs (2013, methodology): “The Laplace transform Ex  e −qτ c −vXτ+ c 1 {τ c <τ − 0 }  , q, v > 0, was computed in Corollary 3 of Ivanovs and Palmowski (2012). The following result is the derivative of this transform at v = 0.”
Exit identities for L\'evy processes observed at Poisson arrival times (2014, methodology): “10] for θ = 0 and [13] for the general case).”