Optimal portfolio theory for stable distributions (Q2740072)

This paper deals with the problem of finding the optimal allocation in the investment portfolio \(x'Z\), where \(x\) is the weight vector, \(Z=(Z_0,Z_1,\ldots,Z_{d})\) is the vector of asset returns, in which \(Z_0\) is the risk free asset return and \(Z_{i}, i=1,\ldots,d,\) is the \(i\)-th risky asset return, the vector of risky asset returns is \(\alpha\)-stable distributed, \(\alpha>1\). The author proposes the numerical method for the solution of the problem \(\min_{x}E(|x'Z-E(x'Z)|^{r}, r\in[1,\alpha]\), where short selling is allowed and the assets have different individual stable parameters.