Fluctuation theory for one-sided Levy processes with a matrix-exponential time horizon

[摘要] There is an abundance of useful fluctuation identities for one-sided Levy processes observed up to an independent exponentially distributed time horizon. We show that all the fundamental formulas generalize to time horizons having matrix exponential distributions, and the structure is preserved. Essentially, the positive killing rate is replaced by a matrix with eigenvalues in the right half of the complex plane which, in particular, applies to the positive root of the Laplace exponent and the scale function. Various fundamental properties of thus obtained matrices and functions are established, resulting in an easy to use toolkit. An important application concerns deterministic time horizons which can be well approximated by concentrated matrix exponential distributions. Numerical illustrations are also provided. (C) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] Functions of matrices;Rational Laplace transform;Scale function;Wiener-Hopf factorization