Next Article in Journal
The Impact of Guarantees on the Performance of Pension Saving Schemes: Insights from the Literature
Next Article in Special Issue
Multivariate Frequency-Severity Regression Models in Insurance
Previous Article in Journal
Combining Alphas via Bounded Regression
Previous Article in Special Issue
Multi-Objective Stochastic Optimization Programs for a Non-Life Insurance Company under Solvency Constraints
Article Menu

Export Article

Open AccessArticle
Risks 2015, 3(4), 491-514; doi:10.3390/risks3040491

On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy

1
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong
2
Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Montserrat Guillén
Received: 9 October 2015 / Accepted: 3 November 2015 / Published: 10 November 2015
View Full-Text   |   Download PDF [799 KB, uploaded 10 November 2015]   |  

Abstract

In the compound Poisson insurance risk model under a dividend barrier strategy, this paper aims to analyze jointly the aggregate discounted claim amounts until ruin and the total discounted dividends until ruin, which represent the insurer’s payments to its policyholders and shareholders, respectively. To this end, we introduce a Gerber–Shiu-type function, which further incorporates the higher moments of these two quantities. This not only unifies the individual study of various ruin-related quantities, but also allows for new measures concerning covariances to be calculated. The integro-differential equation satisfied by the generalized Gerber–Shiu function and the boundary condition are derived. In particular, when the claim severity is distributed as a combination of exponentials, explicit expressions for this Gerber–Shiu function in some special cases are given. Numerical examples involving the covariances between any two of (i) the aggregate discounted claims until ruin, (ii) the discounted dividend payments until ruin and (iii) the time of ruin are presented along with some interpretations. View Full-Text
Keywords: compound Poisson risk model; dividend barrier strategy; aggregate discounted claims until ruin; discounted dividend payments; joint moments; covariance; Gerber–Shiu function compound Poisson risk model; dividend barrier strategy; aggregate discounted claims until ruin; discounted dividend payments; joint moments; covariance; Gerber–Shiu function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Cheung, E.C.; Liu, H.; Woo, J.-K. On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy. Risks 2015, 3, 491-514.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Risks EISSN 2227-9091 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top