Multi-objective portfolio optimization under tempered stable Levy distribution with Copula dependence

Taking into account the leptokurtosis nature of financial returns distribution and the non-linear dependence structure of the underlying assets variables in portfolio, the tempered stable Levy distribution and the Copula function (TS Copula) are employed to describe the multi-objective portfolio optimization problem. In order to investigate the modeling ability of TS distribution coupling with different Copula functions, the model is designed to maximize the benefits while minimizing the risk in finding a set of non-dominant Pareto solutions. The problem of constrained TS Copula multi-objective investment optimization is solved by using three intelligent algorithms, namely the NSGA-II, SPEA-II and MOPSO. Then the empirical studies in Chinese stock markets illustrate that the returns distribution is leptokurtic and heavy tailed. Furthermore, the Skewed-t Copula function coupling with tempered stable marginal distribution can effectively capture the thick tail distribution of portfolio returns and the non-linear asymmetric dependence structure among assets. It is the Skewed-t Copula coupling with tempered stable Levy distribution that gets the best fitting performance. In addition, the MOPSO and NSGA-II intelligent algorithms are effective in solving TS Copula based multi-objective portfolio optimization.

Automated summary

The study utilizes TS Copula to describe multi-objective portfolio optimization, showing that Skewed-t Copula coupled with tempered stable Levy distribution fits financial market data best. Additionally, the MOPSO and NSGA-II algorithms are effective in solving multi-objective portfolio optimization problems based on TS Copula.