We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a large class of forward performance processes, as well as the corresponding optimal portfolios, with power-utility initial data and for stock–factor correlation matrices with eigenvalue equality (EVE) structure, which we introduce here. This is done by solving the associated nonlinear parabolic partial differential equations (PDEs) posed in the “wrong” time direction. Along the way, we establish on domains an explicit form of the generalised Widder theorem of Nadtochiy and Tehranchi (Math. Finance 27:438–470, 2015, Theorem 3.12) and rely for that on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the “right” time direction.

我们考虑在不完全市场中根据远期投资绩效标准进行最优投资组合选择的问题。给定多种交易资产，其价格取决于多个可观察到的随机因素，我们使用功率效用初始数据以及具有特征值相等的库存因子相关矩阵构造一类远期业绩过程以及相应的最优投资组合（EVE）结构，我们在这里介绍。这是通过求解在“错误”时间方向上构成的相关联的非线性抛物线偏微分方程（PDE）来完成的。在此过程中，我们在域上建立Nadtochiy和Tehranchi的广义Widder定理的显式形式（Math。Finance 27：438-470，2015，定理3）。