$L_p$ regularized portfolio optimization

Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact function determines which regularizer is used. We also show that any regularizer based on the norm $L_p$ with $p>1$ makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with $p<1$ do not. The $L_1$ norm represents a bo...