EconPapers    
Economics at your fingertips  
 

A Saddlepoint Approximation to the Distribution of Inhomogeneous Discounted Compound Poisson Processes

Riccardo Gatto ()
Additional contact information
Riccardo Gatto: University of Bern

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 3, 533-551

Abstract: Abstract In this article we propose an accurate approximation to the distribution of the discounted total claim amount, where the individual claim amounts are independent and identically distributed and the number of claims over a specified period is governed by an inhomogeneous Poisson process. More precisely, we compute cumulant generating functions of such discounted total claim amounts under various intensity functions and individual claim amount distributions, and invert them by the saddlepoint approximation. We provide precise conditions under which the saddlepoint approximation holds. The resulting approximation is numerically accurate, computationally fast and hence more efficient than Monte Carlo simulation.

Keywords: Cumulant generating function; Intensity function; Interest rate; Monte Carlo; Shot-noise process; Total claim amount; 60G55; 41A60 (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s11009-008-9116-0 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:12:y:2010:i:3:d:10.1007_s11009-008-9116-0

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

DOI: 10.1007/s11009-008-9116-0

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 ().

 
Page updated 2022-05-12
Handle: RePEc:spr:metcap:v:12:y:2010:i:3:d:10.1007_s11009-008-9116-0