Purchasing Term Life Insurance to Reach a Bequest Goal While Consuming

SIAM Journal on Finance, Forthcoming

31 Pages Posted: 2 Mar 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

S. D. Promislow

York University - Department of Mathematics & Statistics

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: February 26, 2016

Abstract

We determine the optimal strategies for purchasing term life insurance and for investing in a risky financial market in order to maximize the probability of reaching a bequest goal while consuming from an investment account. We extend Bayraktar and Young (2015) by allowing the individual to purchase term life insurance to reach her bequest goal. The premium rate for life insurance, h, serves as a parameter to connect two seemingly unrelated problems. As the premium rate approaches 0, covering the bequest goal becomes costless, so the individual simply wants to avoid ruin that might result from her consumption. Thus, as h approaches 0, the problem in this paper becomes equivalent to minimizing the probability of lifetime ruin, which is solved in Young (2004). On the other hand, as the premium rate becomes arbitrarily large, the individual will not buy life insurance to reach her bequest goal. Thus, as h approaches infinity, the problem in this paper becomes equivalent to maximizing the probability of reaching the bequest goal when life insurance is not available in the market, which is solved in Bayraktar and Young (2015).

Keywords: Term life insurance, bequest motive, consumption, optimal investment, stochastic control

Suggested Citation

Bayraktar, Erhan and Promislow, S. D. and Young, V.R., Purchasing Term Life Insurance to Reach a Bequest Goal While Consuming (February 26, 2016). SIAM Journal on Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2739726 or http://dx.doi.org/10.2139/ssrn.2739726

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

S. D. Promislow

York University - Department of Mathematics & Statistics ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada
(416)736-2100, ext. 33767 (Phone)

HOME PAGE: http://starcraft.ccs.yorku.ca/atlas/servlet/atlas/action/AtlasAction/template/person.vm?eventsubmit_

Virginia R. Young (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

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