论文标题
关于投资组合问题的抛物线方程
On the parabolic equation for portfolio problems
论文作者
论文摘要
我们考虑与有限范围消耗相关的半连接方程 - 随机因子框架下的投资问题，我们证明它可以接受经典的解决方案，并提供了所有强制性估算，以成功地采用验证推理。该纸张涵盖了标准时间添加剂的实用程序以及递归实用程序框架。我们通过考虑更一般的因素动态来扩展现有结果，包括非平地扩散部分以及资产和因素之间的随机相关性。此外，这是第一篇损害金融中许多其他优化问题的论文，例如与冷漠定价或二次对冲问题有关的论文。还提供了结果到随机差异效用和鲁棒投资组合优化的扩展。我们论文的本质在使用改进的随机方法来证明对控制空间受限的合适的HJB方程证明梯度估计值。
We consider a semilinear equation linked to the finite horizon consumption - investment problem under the stochastic factor framework and we prove it admits a classical solution and provide all obligatory estimates to successfully apply a verification reasoning. The paper covers the standard time additive utility, as well as the recursive utility framework. We extend existing results by considering more general factor dynamics including a non-trivial diffusion part and a stochastic correlation between assets and factors. In addition, this is the first paper which compromises many other optimization problems in finance, for example those related to the indifference pricing or the quadratic hedging problem. The extension of the result to the stochastic differential utility and robust portfolio optimization is provided as well. The essence of our paper lays in using improved stochastic methods to prove gradient estimates for suitable HJB equations with restricted control space.
