A multi-dimensional martingale for Markov additive processes and its applications

By Søren Asmussen, Offer Kella. Advances in Applied Probability, 2000

130 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

First Passage of a Markov Additive Process and Generalized Jordan Chains (2010, background): “It has been realized before that the 0s of det(F (α)) with positive real parts and the corresponding null spaces of F(α) play an important role in many problems concerning fluctuations of MAPs; see, for example, [3], [4], and [13].”
A technique for exponential change of measure for Markov processes (2002, methodology): “Following Asmussen and Kella (2000), we have EEh(t) ¼ 1 for all t > 0 and hence Eh(t) is a true martingale.”
First Passage Times for Markov Additive Processes with Positive Jumps of Phase Type (2008, methodology): “As far as the author is aware, the only existing approach to determine the Laplace transform of first passage times for MAPs is the construction of suitable martingales, as proposed in [4] or [16].”
Russian and American put options under exponential phase-type Lévy models (2004, methodology): “We adapt now the semi-Markov generalization of the Kella-Whitt martingale introduced by Asmussen and Kella [7].”
Fluctuations of spectrally negative Markov additive processes (2008, methodology): “The basis of this section is the new martingale introduced by Asmussen and Kella (2000).”