First passage problems for upwards skip-free random walks via the scale functions paradigm. (June 2019)

• Record Type: Journal Article
• Authors: Avram, Florin; Vidmar, Matija
• Is Part Of: Advances in applied probability. Volume 51:Number 2(2019)
• Page Start: 408
• Page End: 424
• Publication Date: 2019-06
• Subjects: Skip-free Markovian jump process, -- random walk, -- scale function, -- martingale, -- compound binomial risk model; Primary 60G50, -- Secondary 91B30; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2019.17
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: In this paper we develop the theory of the W and Z scale functions for right-continuous (upwards skip-free) discrete-time, discrete-space random walks, along the lines of the analogous theory for spectrally negative Lévy processes. Notably, we introduce for the first time in this context the one- and two-parameter scale functions Z, which appear for example in the joint deficit at ruin and time of ruin problems of actuarial science. Comparisons are made between the various theories of scale functions as one makes time and/or space continuous.