The paper analyzes the simulated long-term behavior of well diversified portfolios in continuous financial markets. It focuses on the equi-weighted index and the market portfolio. The paper illustrates that the equally weighted portfolio constitutes a good proxy of the growth optimal portfolio,...

In this paper we analyze the simulated behavior of diversified portfolios in a continuous financial market. In particular, we focus on equally weighted portfolios. We illustrate that these well diversified portfolios constitute good proxies of the growth optimal portfolio. The multi-asset market...

The stable distribution, in its many parametrizations, is central to many stochastic processes. Many random variables that occur in the study of Lévy processes are related to it. Good progress has been made recently for simulating various quantities related to the stable law. In this note, we...

It is well known that fractional Gaussian noise (fGn) generated by synthesizing the fGn autocorrelation structure exhibits exact short and long-term dependence, as well as a good approximation to the theoretical power-law spectrum. In contrast, the spectral synthesis method (SSM), based on...

Fractional Brownian motion (FBM) is a random fractal that has been used to model many one-, two- and multi-dimensional natural phenomena. The increments process of FBM has a Gaussian distribution and a stationary correlation function. The fractional Gaussian process (FGp) algorithm is an exact...