随机因子模型正演过程的构造及Widder定理的推广
Construction of Forward Performance Processes in Stochastic Factor Models and an Extension of Widder's Theorem
摘要：
研究了不完全市场中远期投资绩效准则下的最优投资组合选择问题。给定多个可交易资产，其价格取决于多个可观察的随机因素，我们构建了一个大类的前向性能过程与电力效用的初始数据，以及相应的最优投资组合。这是通过解决相关的非线性抛物型偏微分方程（PDE）提出的“错误”的时间方向，股票因子相关矩阵的特征值相等（EVE）的结构，我们在这里介绍。在此过程中，我们在域上建立了Nadtochiy和Tehranchi [NT15，定理3.12]的广义Widder定理的显式形式，并由此依赖于在“正确”时间方向上提出的适当线性抛物型偏微分方程的解的时间拉普拉斯反演。
英文摘要：
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 with power-utility initial data, as well as the corresponding optimal portfolios. This is done by solving the associated non-linear parabolic partial differential equations (PDEs) posed in the "wrong" time direction, for stock-factor correlation matrices with eigenvalue equality (EVE) structure, which we introduce here. Along the way we establish on domains an explicit form of the generalized Widder's theorem of Nadtochiy and Tehranchi [NT15, Theorem 3.12] and rely hereby on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the "right" time direction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
