Optimal Strategies for Prudent Investors
  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. 
R. Baviera, M. Pasquini, M. Serva, A. Vulpiani (Universit\`a   dell'Aquila and Roma "La Sapienza", Italy)