Handbook of Heavy Tailed Distributions in Finance

3.2 A three fund separation model in the domain of attraction of a stable law

Let us assume that the vector $\mathit{r}=[{\mathit{r}}_1,\text{…},{\mathit{r}}_{\mathit{n}}]\prime$ describes the following three-fund separating stable model of security returns:

$\begin{array}{cc}{r}_i={\mu }_i+b_{i}Y+{\epsilon }_i,& i=1,\dots ,n,\end{array}$

  (27)

where the random vector $\mathit{\epsilon }=({\mathit{\epsilon }}_1,{\mathit{\epsilon }}_2,\text{…},{\mathit{\epsilon }}_{\mathit{n}})\prime$ is independent from Y and follows ajoint sub-Gaussian ${\alpha }_1$-stable distribution $(1<{\alpha }_1<2$