时间不一致控制的弱均衡:在投资退出决策中的应用

IF 1.6 3区 经济学 Q3 BUSINESS, FINANCE Mathematical Finance Pub Date : 2023-04-29 DOI:10.1111/mafi.12391
Zongxia Liang, Fengyi Yuan
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引用次数: 0

摘要

本文考虑了当需要同时制定控制和停止策略时的时间不一致问题(我们称之为停止控制问题)。我们首先在一般多维控制扩散模型下建立了时间不一致的停止控制问题,并提出了其平衡的形式化定义。我们证明了控制-停止策略的可容许对(u,C)$(hat{u},C)是平衡的,当且仅当与之相关的辅助函数求解扩展的HJB系统,提供了一种验证或排除平衡解的方法。我们提供了几个例子来说明数学金融和控制理论的应用。对于报酬函数内生依赖于当前财富的问题,明确地获得了均衡。对于另一个具有非部分折扣的模型,我们证明了任何不变比例策略都不可能是均衡的。我们进一步证明了一般非常平衡的存在性,并用奇异边值问题描述。这个例子表明,考虑我们的组合问题与单独研究它们有本质的不同。最后,我们还提供了一个具有双曲折扣的二维例子。
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Weak equilibria for time-inconsistent control: With applications to investment-withdrawal decisions

This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the time-inconsistent stopping control problems under general multidimensional controlled diffusion model and propose a formal definition of their equilibria. We show that an admissible pair ( u ̂ , C ) $(\hat{u},C)$ of control-stopping policy is equilibrium if and only if the auxiliary function associated with it solves the extended HJB system, providing a methodology to verify or exclude equilibrium solutions. We provide several examples to illustrate applications to mathematical finance and control theory. For a problem whose reward function endogenously depends on the current wealth, the equilibrium is explicitly obtained. For another model with a nonexponential discount, we prove that any constant proportion strategy can not be equilibrium. We further show that general nonconstant equilibrium exists and is described by singular boundary value problems. This example shows that considering our combined problems is essentially different from investigating them separately. In the end, we also provide a two-dimensional example with a hyperbolic discount.

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来源期刊
Mathematical Finance
Mathematical Finance 数学-数学跨学科应用
CiteScore
4.10
自引率
6.20%
发文量
27
审稿时长
>12 weeks
期刊介绍: Mathematical Finance seeks to publish original research articles focused on the development and application of novel mathematical and statistical methods for the analysis of financial problems. The journal welcomes contributions on new statistical methods for the analysis of financial problems. Empirical results will be appropriate to the extent that they illustrate a statistical technique, validate a model or provide insight into a financial problem. Papers whose main contribution rests on empirical results derived with standard approaches will not be considered.
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