Portfolio optimization with CVaR under VG process

Formal portfolio optimization methodologies describe the dynamics of financial instruments price with Gaussian Copula (GC). Without considering the skewness and kurtosis of assets return rate, optimization with GC underestimate the optimal CVaR of portfolio. In the present paper, we develop the approach for portfolio optimization by introducing Lévy processes. It focuses on describing the dynamics of assets' log price with Variance Gamma copula (VGC) rather than GC. A case study for three Indexes of Chinese Stock Market is performed. On application purpose, we calculate the best hedge positions of Shanghai Index (SHI), Shenzhen Index (SZI) and Small Cap Index (SCI) with the performance function CVaR under VG model. It can be combined with Monte Carlo Simulation and nonlinear programming techniques. This framework is suitable for any investment companies.