矩阵值因子模型的长期最优投资
Long Term Optimal Investment in Matrix Valued Factor Models
摘要：
研究了状态变量为矩阵值的因子模型下的长期最优投资问题。得到了明确的参数约束条件，在此条件下，对于等弹性投资者，当投资期限趋近无穷大时，有限期价值函数和最优策略收敛于它们的长期对应值。这种融合也为通用事业带来了投资组合收费公路。通过使用半线性偏微分方程的大时间行为的结果，我们的分析扩展仿射模型，其中的Wishart过程驱动的投资机会，非仿射设置。此外，在仿射设置中，构造了一个示例，其中值函数不是指数仿射的，与具有向量值状态变量的模型相反。
英文摘要：
Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approaches infinity. This convergence also yields portfolio turnpikes for general utilities. By using results on large time behaviour of semi-linear partial differential equations, our analysis extends affine models, where the Wishart process drives investment opportunities, to a non-affine setting. Furthermore, in the affine setting, an example is constructed where the value function is not exponentially affine, in contrast to models with vector-valued state variables.
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