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ON THE DISTRIBUTION OF THE EXCEDENTS OF FUNDS WITH ASSETS AND LIABILITIES IN PRESENCE OF SOLVENCY AND RECOVERY REQUIREMENTS

Published online by Cambridge University Press:  12 April 2018

Benjamin Avanzi ,
Lars Frederik Brandt Henriksen  and
Bernard Wong
Benjamin Avanzi
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney Business School, UNSW Sydney, NSW 2052, Australia Département de Mathématiques et de Statistique, Université de Montréal, Montréal QC H3T 1J4, Canada E-Mail: b.avanzi@unsw.edu.au
Lars Frederik Brandt Henriksen*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark
Bernard Wong
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney Business School, UNSW Sydney, NSW 2052, Australia E-Mail: bernard.wong@unsw.edu.au
*
E-Mail: lars.brandt.henriksen@gmail.com
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Abstract

We consider a profitable, risky setting with two separate, correlated asset and liability processes (first introduced by Gerber and Shiu, 2003). The company that is considered is allowed to distribute excess profits (traditionally referred to as dividends in the literature), but is regulated and is subject to particular regulatory (solvency) constraints. Because of the bivariate nature of the surplus formulation, such distributions of excess profits can take two alternative forms. These can originate from a reduction of assets (and hence a payment to owners), but also from an increase of liabilities (when these represent the wealth of owners, such as in pension funds). The latter is particularly relevant if distributions of assets do not make sense because of the context, such as in regulated pension funds where assets are locked until retirement. In this paper, we extend the model of Gerber and Shiu (2003) and consider recovery requirements for the distribution of excess funds. Such recovery requirements are an extension of the plain vanilla solvency constraints considered in Paulsen (2003), and require funds to reach a higher level of funding than the solvency level (if and after it is triggered) before excess funds can be distributed again. We obtain closed-form expressions for the expected present value of distributions (asset decrements or liability increments) when a distribution barrier is used.

Keywords

Dividendsfunding ratioregulationsolvencyrecovery requirementsC44G24G32G35
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 647 - 672
Copyright
Copyright © Astin Bulletin 2018 

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