模糊厌恶下的终身破产概率最小化
Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion
摘要：
我们确定的最优稳健投资策略的个人谁的目标在一个给定的消费率，并寻求最小化终身破产的概率时，她没有完全的信心，风险资产的漂移。利用随机控制，我们将价值函数刻画为一个相关的Hamilton-Jacobi-Bellman（HJB）方程的唯一经典解，得到了最优投资和漂移失真的反馈形式，并讨论了它们对各种模型参数的依赖性.在分析HJB方程时，我们利用Perron方法建立了黏性解的存在唯一性，然后利用Cole-Hopf变换得到的一个等价的凸问题来提升正则性.我们证明了原始值函数可能会失去凸性的一类参数和Isaacs条件可能失败。数值例子也被包括来说明我们的结果。
英文摘要：
We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky asset. Using stochastic control, we characterize the value function as the unique classical solution of an associated Hamilton-Jacobi-Bellman (HJB) equation, obtain feedback forms for the optimal investment and drift distortion, and discuss their dependence on various model parameters. In analyzing the HJB equation, we establish the existence and uniqueness of viscosity solution using Perron's method, and then upgrade regularity by working with an equivalent convex problem obtained via the Cole-Hopf transformation. We show the original value function may lose convexity for a class of parameters and the Isaacs condition may fail. Numerical examples are also included to illustrate our results.
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