On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion

In this communication, a convenient Laplace transform of the bivariate supremum and the last time the supremum is attained, is established when the underlying Levy process is subordinate Brownian motion with drift. Explicit integral representations of the Laplace transform of the joint supremum and the last time it occurred are derived in terms of the Levy-Khintchine exponent of the subordinator Laplace exponent. As an example, a subordinator with exponential Levy measure is exploited. (C) 2015 Elsevier B.V. All rights reserved.