Equilibrium asset pricing with power utility

与电力公用事业的均衡资产定价

• 批准号: 2585621
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2585621
• 关键词: Equilibrium; asset; pricing; power; utility

The goal of this research project is to characterise the equilibrium dynamics of assets arising in different types of equilibria: with endogenous returns, endogenous volatility, and endogenous interest rates, respectively. The first goal is to study the frictionless case in both complete and incomplete markets and compare this to the extant literature. Whereas the case of exponential utility is by now well understood, see e.g. [2], [3], [6], the case of power utility is largely open. The next goal is then to extend the results to transaction costs. Here the case of mean-variance utilities is well understood, see [1] and [4], and partial results exist for exponential utilities [5].Mathematically, the problem is linked to systems of forward-backward stochastic differential equations. Unlike in the case of exponential utilities, the forward and the backward equations are coupled in the case of power utility. So, an important problem is to prove well-posedness, existence and uniqueness of those FBSDE systems.References:[1] B. Bouchard, M. Fukasawa, M. Herdegen, and J. Muhle-Karbe. Equilibrium returns with transaction costs. Finance and Stochastics, 22:569-601, 2018.[2] Escauriaza, Xing and Schwarz: Radner equilibrium and systems of quadratic BSDEs with discontinuous generators, 2021.[3] P. Guasoni and M. H. Weber. Incomplete-market equilibrium with unhedgeable fundamentals and heterogenous agents. Michael J. Brennan Irish Finance Working Paper Series, 2022.[4] M. Herdegen, J. Muhle-Karbe and D. Possamai: Equilibrium asset pricing with transaction costs, Finance and Stochastics, 25:231-275, 2021.[5] M. Herdegen and J. Muhle-Karbe: Stability of Radner equilibria with respect to small frictions, Finance and Stochastics, 22:443-502, 2018.[6] C. Kardaras, H. Xing, and G. Zitkovic. Incomplete stochastic equilibria with exponential utilities close to pareto optimality. Stochastic Analysis, Filterting and Stochastic Optimisation, pages 267-292, 2022.

本研究项目的目标是描述不同类型均衡中资产的均衡动态：分别具有内生收益、内生波动和内生利率。第一个目标是研究完全和不完全市场中的无摩擦情况，并将其与现有文献进行比较。虽然指数效用的情况现在已经很好地理解了，参见例如[2]，[3]，[6]，但幂效用的情况在很大程度上是开放的。下一个目标是将结果扩展到交易成本。在这里，均值-方差效用的情况是很好理解的，参见[1]和[4]，并且指数效用存在部分结果[5]。在数学上，该问题与前向-后向随机微分方程系统有关。与指数效用的情况不同，在幂效用的情况下，前向和后向方程是耦合的。因此，一个重要的问题是证明这类FBB-R系统的适定性、存在性和唯一性。Bouchard，M. M. Herdegen，and J. Muhle-Karbe.有交易成本的均衡收益。Finance and Stochastics，22：569-601，2018。[2]Escauriaza，Xing和施瓦茨：Radner平衡和具有不连续生成元的二次BSDEs系统，2021。[3]P. Guasoni和M. H.韦伯不完全市场均衡与不可对冲的基本面和异质代理。迈克尔·布伦南爱尔兰金融工作文件系列，2022年。[4]M. Herdegen，J. Muhle-Karbe和D. Possamai：Equilibrium Asset Pricing with transaction costs，Finance and Stochastics，25：231-275，2021. [5]M. Herdegen和J. Muhle-Karbe：Radner均衡相对于小摩擦的稳定性，金融和随机，22：443-502，2018。[6]C. Kardaras，H. Xing，G.兹科维奇指数效用接近帕累托最优的不完全随机均衡。随机分析，过滤和随机优化，第267-292页，2022年。