Research on risk measure with multiple risk preference and portfolio optimization

In order to reflect investors´ multiple risk attitude towards to capital gains distribution corresponding to the risk, this paper presents a new risk measure, which can make the measured risk be monotonic, translation regressive and non-linear additive. Monotonicity and translation regressive reflect risk measure´s basic economic sense, and non-linear additivity describes the investors´ multiple preferences to different direction fluctuations of capital gains. Investors´ risk attitude towards to negative fluctuations of the return on assets can be described by the non-linear additivity´s local time additive, while investors´ risk attitude towards to positive fluctuations in return on assets can be described by the non-linear additivity´s local super-additivity. Furthermore, this paper builds the portfolio optimization model t combining with the risk measure method, and analyzes the impact of the investors´ multiple risk attitude for the investment strategies. The results show that when the investors are more preferred to obtain excess returns, they should take the centralized investment strategies, while when the investors are more preferred to avoid the loss, they should take the decentralized investment strategies.