Discrete–Time Optimal Execution Under a Generalized Price Impact Model With Markovian Exogenous Orders
Discrete–Time Optimal Execution Under a Generalized Price Impact Model With Markovian Exogenous Orders
复制标题
马尔可夫外生订单广义价格影响模型下的离散时间最优执行
DOI：
10.2139/ssrn.3714066
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Makoto Shimoshimizu
中科院分区：
文献类型：
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作者：
M. Fukasawa;M. Ohnishi;Makoto Shimoshimizu
本文研究了具有广义价格影响的离散时间最优交易执行问题。我们扩展了最近讨论的一个模型，该模型考虑了由小型交易者和大型交易者构成的总随机交易订单对价格的影响。相反，假设总交易量提交的小交易者是连续独立的，本文允许马尔可夫依赖。
我们的新问题是制定为一个马尔可夫决策过程的状态变量，包括最后的小交易者的总订单。在有限的时间范围内，具有恒定绝对风险厌恶（CARA）von Neumann-Morgenstern（vN-M）效用函数的大型交易者最大化最终财富的预期效用。运用动态规划的逆向归纳法，刻画了最优价值函数和最优交易执行策略，得出了最优交易执行策略是三个状态变量的时间依赖仿射函数的结论.此外，数值分析普遍认为，最佳执行策略承认一个'统计套利'通过往返交易，虽然我们的模型认为一个线性的永久价格影响，不承认任何价格操纵或套利。原因是我们的模型考虑了小交易者的订单与马尔可夫依赖引起的价格影响。
This paper examines a discrete-time optimal trade execution problem with generalized price impact. We extend a model recently discussed, which considers price impacts of aggregate random trade orders posed by small traders as well as a large trader. In contrast that assumes aggregate trading volumes submitted by small traders are serially independent, this paper allows a Markovian dependence.
Our new problem is formulated as a Markov decision process with state variables including the last small traders' aggregate orders. Over a finite horizon, the large trader with Constant Absolute Risk Aversion (CARA) von Neumann-Morgenstern (vN-M) utility function maximizes the expected utility from the final wealth. By applying the backward induction method of dynamic programming, we characterize the optimal value function and optimal trade execution strategy, and conclude that the execution strategy is a time-dependent affine function of three state variables. Moreover, numerical analysis prevails that the optimal execution strategy admits a `statistical arbitrage' via a round-trip trading, although our model considers a linear permanent price impact, which does not admit any price manipulation or arbitrage. The reason is that our model considers price impacts caused by small traders' orders with a Markovian dependence.
离散时间设置中具有广义价格影响的最优执行问题
DOI：
--
发表时间：
2020
期刊：
Research Institute for Mathematical Sciences (RIMS) Kokyuroku
影响因子：
--
作者：
Fukasawa;M.;Ohnishi;M.;Shimoshimizu;M.
通讯作者：
M.