Optimal Strategies for Prudent Investors
arXiv:cond-mat/9804297
Abstract
We consider a stochastic model of investment on an asset of a stock market for a prudent investor. She decides to buy permanent goods with a fraction $\a$ of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed $\a$. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.
14 pages, LaTeX, epsfig.sty, 7 eps figures, minor changes; accepted for International J. of Theoretical and Applied Finance