Exit Times, Overshoot and Undershoot for a Surplus Process in the Presence of an Upper Barrier

Michael V. Boutsikas () and Konstadinos Politis
Additional contact information
Michael V. Boutsikas: University of Piraeus
Konstadinos Politis: University of Piraeus

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 1, 75-95

Abstract: Abstract We study the movement of a surplus process with initial capital u in the presence of two barriers: a lower barrier at zero and an upper barrier at b (b > u). More specifically, we consider the behaviour of the surplus: (a) in continuous time; and (b) only at claim arrival times. For each of these cases, we find the expected time until the process exits the interval [0,b]. We also obtain results related to the undershoot and overshoot of the surplus which, in particular for case (b) above, are derived under the assumption that the distribution of claim sizes and/or claim interarrival times belongs to the mixed Erlang class. In the final section we discuss the implementation of the methods in a number of examples using computer algebra software. These examples illustrate the efficiency of the methods even in fairly complicated cases.

Keywords: Ruin probability; Sparre Andersen model; Barrier problems; Overshoot; Undershoot; Exit times; Mixed Erlang class; 60K05; 60G40; 60K10; 60G50 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-015-9459-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9459-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-015-9459-2

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().