On different aspects of portfolio optimization

Different aspects for the portfolio optimization (PO) problem are considered. The first aspect is multi-objective optimization. The second is dynamical re-balancing. The third is the evolutionary game aspect (Pioneered by Hens and Schenk-Hoppe [T. Hens, Schenk-Hoppe, Evolutionary stability of portfolio rules in incomplete market, J. Math. Econ. 41 (2005) 43–66].) since portfolio payoff depends not only on the investor’s strategy but also on the other investors’ strategies. We argue that both the different aspects included in the PO study and the basic assumptions made, significantly affect the outcome of the result For example the stochastic effects of mistakes and the change in players numbers are expected to change the results of Hens and Schenk-Hoppe.