英文标题：
《A state-constrained differential game arising in optimal portfolio
liquidation》
---
作者：
Alexander Schied and Tao Zhang
---
最新提交年份：
2015
---
英文摘要：
We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed-form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.
---
中文摘要：
我们考虑在Almgren-Chriss市场影响模型中竞争流动性的n美元风险厌恶型代理人。从数学上讲，这种情况可以用一个具有状态约束的线性二次微分对策的纳什均衡来描述。状态约束作为有限和无限时间范围的终端边界条件进入问题。我们证明了纳什均衡的存在唯一性，并在一些特殊情况下给出了闭式解。我们还分析了均衡策略的定性性质，并给出了相应的财务解释。
---
分类信息：

一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
--
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
--

---
PDF下载：
-->