Minimizing the probability of lifetime drawdown under constant consumption

Bahman Angoshtari, Erhan Bayraktar and Virginia R. Young

Insurance: Mathematics and Economics, 2016, vol. 69, issue C, 210-223

Abstract: We assume that an individual invests in a financial market with one riskless and one risky asset, with the latter’s price following geometric Brownian motion as in the Black–Scholes model. Under a constant rate of consumption, we find the optimal investment strategy for the individual who wishes to minimize the probability that her wealth drops below some fixed proportion of her maximum wealth to date, the so-called probability of lifetime drawdown. If maximum wealth is less than a particular value, m∗, then the individual optimally invests in such a way that maximum wealth never increases above its current value. By contrast, if maximum wealth is greater than m∗ but less than the safe level, then the individual optimally allows the maximum to increase to the safe level.

Keywords: Optimal investment; Stochastic optimal control; Probability of drawdown; Optimal controller-stopper problem; Duality argument; And free-boundary problem (search for similar items in EconPapers)
JEL-codes: D14 D81 G11 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167668715301463
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Minimizing the Probability of Lifetime Drawdown under Constant Consumption (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:69:y:2016:i:c:p:210-223

DOI: 10.1016/j.insmatheco.2016.05.007

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

More articles in Insurance: Mathematics and Economics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().