Maximizing the utility of consumption with commutable life annuities
AbstractThe purpose of this paper is to reveal the relation between commutability of life annuities and retirees’ willingness to annuitize. To this end, we assume the existence of commutable life annuities, whose surrender charge is a proportion of their actuarial value. We model a retiree as a utility-maximizing economic agent who can invest in a financial market with a risky and a riskless asset and who can purchase or surrender commutable life annuities. We define the wealth of an individual as the total value of her risky and riskless assets, which is required to be non-negative during her lifetime. We exclude the actuarial value of her annuity income in calculating wealth; therefore, we do not allow the individual to borrow from her future annuity income because this income is contingent on her being alive.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 51 (2012)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/inca/505554
Commutable annuities; Utility maximization; Retirement; Optimal investment; Optimal consumption; Stochastic control; Impulse control; Singular control; Free-boundary problem;
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- Dixit, Avinash, 1991. "A simplified treatment of the theory of optimal regulation of Brownian motion," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 657-673, October.
- Hyeng Keun Koo, 1998. "Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 49-65.
- Jérôme Detemple & Angel Serrat, 2003. "Dynamic Equilibrium with Liquidity Constraints," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 597-629.
- Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
- He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer, vol. 3(4), pages 663-96, October.
- Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
- Thomas Davidoff & Jeffrey R. Brown & Peter A. Diamond, 2005.
"Annuities and Individual Welfare,"
American Economic Review,
American Economic Association, vol. 95(5), pages 1573-1590, December.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
- Wang, Ting & Young, Virginia R., 2012. "Optimal commutable annuities to minimize the probability of lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 200-216.
- Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
- Bayraktar, Erhan & Hu, Xueying & Young, Virginia R., 2011.
"Minimizing the probability of lifetime ruin under stochastic volatility,"
Insurance: Mathematics and Economics,
Elsevier, vol. 49(2), pages 194-206, September.
- Erhan Bayraktar & Xueying Hu & Virginia R. Young, 2010. "Minimizing the Probability of Lifetime Ruin under Stochastic Volatility," Papers 1003.4216, arXiv.org, revised May 2011.
- Lee Lockwood, 2012.
"Bequest Motives and the Annuity Puzzle,"
Review of Economic Dynamics,
Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 226-243, April.
- Lee Lockwood, 2011. "Code files for "Bequest Motives and the Annuity Puzzle"," Computer Codes 10-110, Review of Economic Dynamics.
- Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
- Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
- Shlomo Benartzi & Alessandro Previtero & Richard H. Thaler, 2011. "Annuitization Puzzles," Journal of Economic Perspectives, American Economic Association, vol. 25(4), pages 143-64, Fall.
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