Interest Rates and Transaction Costs in Incomplete Equilibria

金融模型的一个典型起点是给定资产价格，并操纵它来确定结果。 一个研究较少的路径是问什么使资产定价模型好，这样好的模型从何而来？ 均衡理论研究资产定价模型的形成在一个经济的总供给满足其总需求的基本水平。该奖项将研究两个在不完全环境中设置的总体均衡项目，其中并非所有风险都可以通过交易来捕获。 这些项目使用数学工具来描述基于均衡的“良好”模型，这些模型涉及（一）利率的形成，以及（二）存在比例交易成本的股票价格的形成。 利率和交易成本都与金融市场高度相关，但目前在不完全均衡环境中却知之甚少。该奖项将涉及研究生的合作、参与和培训。该奖项将研究两个相关的问题，涉及数学金融中的随机系统的平衡。 第一个目标是证明具有随机利率和比例交易费用的不完全市场模型中有限代理人Radner均衡的存在性。 在获得存在性之后，研究者将分析不完全性对内生决定的资产价格的影响。 在数学上，分析来自完全耦合的二次倒向随机微分方程（BDED）系统，这是双重反射的情况下的交易成本。 存在的结果，这样的BAPONS系统是非建设性的，这复杂化的不完整性effects.This奖项的分析反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

A typical starting point for a financial model takes an asset price as given and manipulates it to determine results. A less studied path asks what makes an asset pricing model good, and where do such good models come from? Equilibrium theory studies the formation of asset pricing models at a fundamental level where an economy's total supply meets its total demand. This award will study two overarching equilibrium projects set in incomplete settings, where not all risk can be captured by trading. The projects use mathematical tools that are now within reach to describe equilibrium-based "good" models involving (i) the formation of interest rates, and (ii) the formation of stock prices in the presence of proportional transaction costs. Both interest rates and transaction costs are highly relevant to financial markets but currently poorly understood in incomplete equilibrium settings. The award will involve collaborations and the involvement and training of graduate students. This award will study two related problems involving equilibrium of stochastic systems in mathematical finance. The first goal is to prove the existence of a finite-agent Radner equilibrium in incomplete market models with stochastic interest rates and proportional transaction costs. After obtaining existence, the investigator will analyze the effects of incompleteness on the endogenously determined asset prices. Mathematically, the analysis draws from systems of fully coupled quadratic backward stochastic differential equations (BSDE), which are doubly reflective in the case of transaction costs. Existence results for such BSDE systems are nonconstructive, which complicates the analysis of incompleteness effects.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.