V aR 之下厚尾分布的最优资产组合的收敛性

主要研究在V aR 风险度量之下, 收益具有厚尾性质的资产的投资组合问题. 证明了基于尾部分布二阶展开的最优投资组合收敛于基于尾部分布一阶展开的最优投资组合. 因此, 对于V aR 风险度量之下的最优投资组合问题, 如果要求的风险承受水平充分低, 则只需要利用尾部分布的一阶展开代替厚尾部分布进行近似计算, 就可以达到满意的精度, 从而不需要进行复杂的高阶运算.

Convergence of optimal portfol io under VaR with fat ta ils

The paper studies the po rtfo lio op t im izat ion p rob lem under V aR m easu re w here thedist ribu t ion s of retu rn s are of fat tails. It has p roved that the op t im al po rtfo lio based on the secondo rder fat tails converges to the op t im al po rtfo lio based on the f irst o rder fat tails. The resu lt show sthat it need on ly con st ruct the op t im al po rtfo lio based on the f irst o rder fat tails w h ich is enough toguaran tee a good app rox im at ing accu racy w hen the requ ired risk level is suff icien t low. Thu s thecomp lex compu tat ion fo r the po rtfo lio op t im izat ion w ith h igher o rder fat tails can be avo ided.