基于修正的χ~2-散度的不确定投资组合优化

Uncertain portfolio optimization based on modified χ~2-divergence

随着我国金融体系的不断完善,投资渠道呈现出多样化的发展.但由于市场变化、政策修改、企业经营等不确定因素,如何选择最优的投资方式以平衡风险和收益的比例要求成为投资者关注的焦点.投资组合的方法选择可以为投资的相关决策提供重要依据.首先提出不确定条件下的投资组合问题,利用经验分布和未知分布修正的χ2-散度距离来构造未知分布集合,再利用测度转化将不确定参数对未知分布问题转化为似然比对于经验分布的凸优化问题,然后应用拉格朗日对偶理论得到投资组合问题的等价形式.

With the continuous improvement of Chinese financial system,the investment channels showed diversified development.However,due to the uncertain factors such as market change,policy revision,enterprise management and so on,how to choose the optimal investment mode to balance the proportion of risks and benefits has become the focus of investors.The method selection of investment portfolio can provide important basis for investment decision.The portfolio problem was first given under uncertain conditions,the set of unknown distribution was constructed by using the modified χ^2-divergence distance of empirical distribution and unknown distribution,and the problem of uncertain parameters to unknown distribution was transformed into the convex optimization problem of likelihood ratio to empirical distribution by measure transformation,and then the equivalent form of portfolio problem was obtained by using Lagrange duality theory.