英文标题：
《Markovian Nash equilibrium in financial markets with asymmetric
information and related forward-backward systems》
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作者：
Umut \\c{C}etin, Albina Danilova
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最新提交年份：
2016
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英文摘要：
This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward-backward system of partial and stochastic differential equations. In particular, the price set by the market makers solves a nonstandard \"quadratic\" backward stochastic differential equation. The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models.
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中文摘要：
本文发展了一种新的方法来研究具有不对称信息主体的金融市场中的连续时间纳什均衡。这种方法允许我们解除当前文献对做市商风险中性的限制。结果表明，当做市商规避风险时，代理人的最优策略是偏微分方程组和随机微分方程组的正倒向解。特别是，做市商设定的价格解决了一个非标准的“二次”倒向随机微分方程。本文的主要结果是通过绝对连续分布函数空间上的一个不动点变元，在任意时间区间上证明了该系统的马尔可夫解的存在性。此外，本文得到的均衡能够解释当前不对称信息模型无法捕捉的几个典型事实。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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