Log-robust portfolio management

We present a robust optimization approach to portfolio management under uncertainty that (i) builds upon the well-established Lognormal model for stock prices while addressing its limitations, and (ii) incorporates the imperfect knowledge on the true distribution of the continuously compounded rates of return, i.e., the increments of the logarithm of the stock prices, in an intuitive manner. We derive theoretical insights into the worst-case uncertainty and the optimal allocation, in the cases with and without short sales.