Optimal portfolios of a small investor in a limit order market: a shadow price approach
Optimal portfolios of a small investor in a limit order market: a shadow price approach
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限价订单市场中小投资者的最优投资组合：影子价格法
DOI：
10.1007/s11579-010-0027-9
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发表时间：
2010
影响因子：
1.6
通讯作者：
Maximilian Stroh
中科院分区：
文献类型：
--
作者：
C. Kühn;Maximilian Stroh
研究了限价订单市场中的Merton组合优化问题。在限价订单市场上交易的投资者可以在允许立即交易的市场订单和以更优惠的价格交易但只有在另一个市场参与者下相应的市场订单时才执行的限价订单之间进行选择。假设来自其他交易者的市场订单泊松到达，我们使用影子价格方法，类似于Kallsen和Muhle-Karbe （Ann Appl Probab，即将发布）对具有比例交易成本的模型，以表明最优策略包括使用市场订单将投资于风险资产的财富比例保持在一定范围内，类似于比例交易成本的结果。在这些范围内，限价指令是用来从买卖价差中获利的。虽然给定的最优买入价和最优卖出价过程是几何布朗运动，但由此产生的影子价格过程具有跳跃。
We study Merton’s portfolio optimization problem in a limit order market. An investor trading in a limit order market has the choice between market orders that allow immediate transactions and limit orders that trade at more favorable prices but are executed only when another market participant places a corresponding market order. Assuming Poisson arrivals of market orders from other traders we use a shadow price approach, similar to Kallsen and Muhle-Karbe (Ann Appl Probab, forthcoming) for models with proportional transaction costs, to show that the optimal strategy consists of using market orders to keep the proportion of wealth invested in the risky asset within certain boundaries, similar to the result for proportional transaction costs, while within these boundaries limit orders are used to profit from the bid–ask spread. Although the given best-bid and best-ask price processes are geometric Brownian motions the resulting shadow price process possesses jumps.