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

  • Benjamin Avanzi (a1) (a2), Lars Frederik Brandt Henriksen (a3) and Bernard Wong (a4)
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.

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Corresponding author
E-Mail: lars.brandt.henriksen@gmail.com
References
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Albrecher, H. and Thonhauser, S. (2009) Optimality results for dividend problems in insurance. RACSAM Revista de la Real Academia de Ciencias; Serie A, Mathemáticas, 100 (2), 295320.
Asmussen, S. and Albrecher, H. (2010) Ruin Probabilities, Advanced Series on Statistical Science and Applied Probability, 2nd Edition. Vol. 14. Singapore: World Scientific.
Australian Actuaries Institute (31 May 2016) Cross-practice target capital working group: Information note: Target capital (life and GI). Tech. rep., Institute of Actuaries of Australia.
Avanzi, B. (2009) Strategies for dividend distribution: A review. North American Actuarial Journal, 13 (2), 217251.
Avanzi, B., Henriksen, L.F.B. and Wong, B. (2017) Optimal dividends in an asset-liability surplus model under solvency considerations. UNSW Australia Business School Research Paper Series No 2017ACTL01.
Avanzi, B., Tu, V.W. and Wong, B. (2016) A note on realistic dividends in actuarial surplus models. Risks, 4 (4), 37.
Avanzi, B. and Wong, B. (2012) On a mean reverting dividend strategy with Brownian motion. Insurance: Mathematics and Economics, 51 (2), 229238.
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Grundlehren der mathematischen Wissenschaften. Berlin, Heidelberg, New York: Springer-Verlag.
Chen, P. and Yang, H. (2010) Pension funding problem with regime-switching geometric brownian motion assets and liabilities. Applied Stochastic Models in Business and Industry, 26 (2), 125141.
de Finetti, B. (1957) Su un'impostazione alternativa della teoria collettiva del rischio. Transactions of the XVth International Congress of Actuaries, 2, 433443.
Decamps, M., Schepper, A.D. and Goovaerts, M. (2006) A path integral approach to asset-liability management. Physica A: Statistical Mechanics and its Applications, 363 (2), 404416.
Decamps, M., Schepper, A.D. and Goovaerts, M. (2009) Spectral decomposition of optimal asset-liability management. Journal of Economic Dynamics and Control, 33 (3), 710724.
Gerber, H.U. (1972) Games of economic survival with discrete- and continuous-income processes. Operations Research, 20 (1), 3745.
Gerber, H.U. (1974) The dilemma between dividends and safety and a generalization of the Lundberg–Cramér formulas. Scandinavian Actuarial Journal, 1974, 4657.
Gerber, H.U. and Shiu, E.S.W. (2003) Geometric brownian motion models for assets and liabilities: From pension funding to optimal dividends. North American Actuarial Journal, 7 (3), 3756.
Müller, P. and Wagner, J. (2017) The impact of pension funding mechanisms on the stability and payoff from Swiss dc pension schemes: A sensitivity analysis. The Geneva Papers on Risk and Insurance - Issues and Practice, 42 (32), 423452.
Paulsen, J. Oct. (2003) Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics, 7 (4), 457473.
Sethi, S.P. and Taksar, M.I. (2002) Optimal financing of a corporation subject to random returns. Mathematical Finance, 12 (2), 155172.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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