Minimizing the Probability of Lifetime Drawdown under Constant Consumption
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 BlackScholes 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 socalled probability of {\it 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2015
 arXiv:
 arXiv:1507.08713
 Bibcode:
 2015arXiv150708713A
 Keywords:

 Quantitative Finance  Portfolio Management;
 Mathematics  Optimization and Control;
 Mathematics  Probability
 EPrint:
 To appear in Insurance: Mathematics and Economics. Keywords: Optimal investment, stochastic optimal control, probability of drawdown. arXiv admin note: text overlap with arXiv:0806.2358