论文标题
默顿问题的基本方法
An elementary approach to the Merton problem
论文作者
论文摘要
在本文中，我们考虑了恒定参数黑色-Scholes-Merton Market for具有恒定相对风险的代理商的无限摩尔顿投资消费问题。经典原始方法是写下候选价值功能并使用验证论点来证明这是解决问题的解决方案。但是，问题的特征将其超出了随机控制的标准设置之外，现有的原始验证证明依赖于参数限制（尤其是但不仅是R <1），对可允许策略空间的限制或复杂的近似参数。 本文的目的是证明可以使用涉及效用函数的随机扰动的简单而优雅的论点来克服这些并发症。
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write down a candidate value function and to use a verification argument to prove that this is the solution to the problem. However, features of the problem take it outside the standard settings of stochastic control, and the existing primal verification proofs rely on parameter restrictions (especially, but not only, R<1), restrictions on the space of admissible strategies, or intricate approximation arguments. The purpose of this paper is to show that these complications can be overcome using a simple and elegant argument involving a stochastic perturbation of the utility function.
