On the Distribution of the Excedents of Funds with Assets and Liabilities in Presence of Solvency and Recovery Requirements

21 Pages Posted: 17 Aug 2016 Last revised: 16 Dec 2016

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Lars Frederik Brandt Henriksen

University of Copenhagen

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: August 17, 2016

Abstract

In this paper, 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. The optimal barrier level, as well as its existence and uniqueness are discussed.

Keywords: Optimal dividends, Funding ratio, Stochastic Control, Regulation, Solvency, Recovery requirements

JEL Classification: C44, G24, G32, G35

Suggested Citation

Avanzi, Benjamin and Heriksen, Lars Frederik Brandt and Wong, Bernard, On the Distribution of the Excedents of Funds with Assets and Liabilities in Presence of Solvency and Recovery Requirements (August 17, 2016). UNSW Business School Research Paper No. 2016ACTL03. Available at SSRN: https://ssrn.com/abstract=2824887 or http://dx.doi.org/10.2139/ssrn.2824887

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

Lars Frederik Brandt Heriksen (Contact Author)

University of Copenhagen ( email )

Universitetsparken 5
Copenhagen, DK-2100
Denmark

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

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