2015/07/30 by Bahman Angoshtari, Erhan Bayraktar, Angoshtari, Bahman +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Financial Markets and Investment Strategies #Optimization and Control (math.OC) #Portfolio Management (q-fin.PM) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1507.08713
openalex publication_date 2015/07/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We assume that an individual invests in a financial market with one riskless\nand one risky asset, with the latter's price following geometric Brownian\nmotion as in the Black-Scholes model. Under a constant rate of consumption, we\nfind the optimal investment strategy for the individual who wishes to minimize\nthe probability that her wealth drops below some fixed proportion of her\nmaximum wealth to date, the so-called probability of it lifetime drawdown.\nIf maximum wealth is less than a particular value, m^*, then the individual\noptimally invests in such a way that maximum wealth never increases above its\ncurrent value. By contrast, if maximum wealth is greater than m^* but less\nthan the safe level, then the individual optimally allows the maximum to\nincrease to the safe level.\n