An optimal consumption problem for general factor models
An optimal consumption problem for general factor models
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一般因子模型的最优消耗问题
DOI：
10.1137/17m1135864
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发表时间：
2018
影响因子：
2.2
通讯作者：
Hideo Nagai and Shuenn-jyi Sheu
中科院分区：
文献类型：
--
作者：
Hiroaki Hata;Hideo Nagai and Shuenn-jyi Sheu
我们考虑有限时间范围内的默顿消费问题，以优化风险规避情况下消费和终端财富的贴现预期电力效用。资产的收益和波动是随机的，受一些经济因素的影响，建模为扩散过程。这个问题变成了一个标准的随机控制问题。我们推导了Hamilton- Jacobi- Bellman （HJB）方程，并研究了它的解。在一般条件下，构造了一个合适的亚解—上解对。证明了该HJB方程解的存在唯一性。最后，给出了验证定理。
We consider the Merton consumption problem on a finite time horizon to optimize the discounted expected power utility of consumption and terminal wealth in risk-averse cases. The returns and volatilities of the assets are random and affected by some economic factors, modeled as a diffusion process. The problem becomes a standard stochastic control problem. We derive the Hamilton--Jacobi--Bellman (HJB) equation and study its solutions. Under general conditions we construct a suitable subsolution--supersolution pair. We prove the existence and uniqueness of solution for this HJB equation. Finally, we show the verification theorem.