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REACHING A BEQUEST GOAL WITH LIFE INSURANCE: AMBIGUITY ABOUT THE RISKY ASSET'S DRIFT AND MORTALITY'S HAZARD RATE

Published online by Cambridge University Press:  05 December 2019

Xiaoqing Liang  and
Virginia R. Young
Xiaoqing Liang
Affiliation:
School of Sciences, Hebei University of Technology, Tianjin 300401, P. R. China, E-Mail: liangxiaoqing115@hotmail.com
Virginia R. Young*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA, E-Mail: vryoung@umich.edu
*
E-Mail: vryoung@umich.edu
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Abstract

We determine the optimal robust strategy of an individual who seeks to maximize the (penalized) probability of reaching a bequest goal when she is uncertain about the drift of the risky asset and her hazard rate of mortality. We assume the individual can invest in a Black–Scholes market. We solve two optimization problems with ambiguity. The first is to maximize the penalized probability of reaching a bequest goal without life insurance in the market. In the second problem, in addition to investing in the financial market, the individual is allowed to purchase term life insurance to help her reach her bequest goal. As the individual becomes more ambiguity averse concerning the drift of the risky asset, she becomes more conservative with her investment strategy. Also, as she becomes more ambiguity averse about her hazard rate of mortality, numerical work indicates she is more likely to buy life insurance when the ambiguity towards the return of the risky asset is not too large.

Keywords

Bequest motiveoptimal investmentterm life insuranceambiguity aversionstochastic controlrobust controlpenalized probabilityC61C73D81G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 187 - 221
Copyright
© Astin Bulletin 2019 

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Footnotes

*

X. Liang thanks the National Natural Science Foundation of China (11701139, 11571189) and the Natural Science Foundation of Hebei Province (A2018202057) for the financial support of her research.

†

V. Young thanks the Cecil J. and Ethel M. Nesbitt Professorship for the partial financial support of her research.

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