随机市场深度下基于风险管理和交易约束的最优执行问题

doi:10.16381/j.cnki.issn1003-207x.2023.1408

Abstract

Abstract:

As an investment decision-making problem， the optimal execution problem is a topic of considerable interest among finance scholars and professionals. Simultaneously， these realistic factors—stochastic market liquidity， investors' aversion to execution risk， and regulatory restrictions on trading behavior—all significantly influence the optimal trading strategies. Therefore， building on the assumption of stochastic market depth， the optimal execution problem with trading constraints encountered by investors exhibiting constant absolute risk aversion （CARA） utility is investigated. Following the market dynamics of the limit order book （LOB）， an optimal execution model is constructed， taking into account risk management and trading constraints. Subsequently， an analytic execution strategy is presented using the dynamic programming approach. The results show that rational investors avoid placing orders in opposite directions simultaneously， and the optimal strategy is characterized by a piecewise linear function of the remaining order quantity. The numerical examples suggest risk-averse investors tend to execute large orders early in the trading period to avoid risk， compared to risk-neutral investors. Furthermore， aside from effectively managing the risk of asset price changes and stochastic fluctuations in liquidity， this model has also proven its capability to enhance the effectiveness of execution strategies. Additionally， market depth and trading constraints play significant roles in influencing both execution risk and the effectiveness of the strategy. In summary， the results emphasize the importance of accounting for both stochastic market liquidity and trading constraints when addressing the optimal execution problem for risk-averse investors.

Key words: limit order book, stochastic market liquidity, optimal execution problem, CARA utility, two-sided trading

CLC Number:

F830.9

Weiping Wu, Yu Lin, Chengneng Jin, Zhenpeng Tang. Constrained Optimal Risk Sensitive Execution Problem with Stochastic Market Depth[J]. Chinese Journal of Management Science, 2025, 33(8): 14-25.

Figures/Tables 9

$θ 0 a$	模型	标准差( $104$ )	偏度	峰度	极差( $105$ )	执行夏普比率( $102$ )
1200	$P 1$	1.19	-0.11	2.96	0.92	3.06
	$P 2$	3.08	0.72	3.76	2.58	1.25
	$P d$	4.93	0.13	2.35	2.72	0.71
1500	$P 1$	1.04	-0.30	2.66	0.67	2.73
	$P 2$	2.43	0.71	3.77	2.23	1.27
	$P d$	4.23	0.14	2.30	2.24	0.65
1800	$P 1$	0.98	-0.35	2.52	0.60	2.39
	$P 2$	2.00	0.70	3.74	1.79	1.28
	$P d$	3.69	0.14	2.24	1.89	0.61
2100	$P 1$	0.95	-0.40	2.65	0.57	2.07
	$P 2$	1.75	0.69	3.71	1.59	1.26
	$P d$	3.27	0.16	2.23	1.65	0.58

$α k$	模型	标准差( $104$ )	偏度	峰度	极差( $105$ )	执行夏普比率( $102$ )
0.30	$P 1$	2.71	-0.33	2.49	1.59	1.06
	$P 2$	2.79	0.63	3.44	2.30	1.10
	$P d$	3.92	0.14	2.34	2.17	0.72
0.40	$P 1$	1.33	-0.72	3.47	0.91	2.16
	$P 2$	2.56	0.68	3.64	2.14	1.20
	$P d$	4.19	0.13	2.29	2.22	0.66
0.50	$P 1$	1.04	-0.30	2.66	0.67	2.73
	$P 2$	2.43	0.71	3.77	2.23	1.27
	$P d$	4.23	0.14	2.30	2.24	0.65
0.60	$P 1$	0.98	-0.29	2.75	0.69	2.92
	$P 2$	2.42	0.74	3.86	2.12	1.27
	$P d$	4.23	0.14	2.29	2.24	0.65

( $10 - 7$ ) $ϕ$	标准差( $104$ )	偏度	峰度	极差( $105$ )	执行夏普比率( $102$ )
2	1.04	-0.30	2.66	0.67	2.73
12	1.05	-0.30	2.64	0.69	2.73
22	1.05	-0.30	2.64	0.67	2.72
32	1.05	-0.32	2.66	0.66	2.71

( $10 - 4$ ) $σ 2$	标准差( $104$ )	偏度	峰度	极差( $105$ )	执行夏普比率( $102$ )
1	1.04	-0.30	2.66	0.67	2.73
2	1.98	-0.88	3.66	1.15	1.33
3	3.31	-0.71	2.60	1.55	0.75
4	4.07	0.31	2.00	1.72	0.57

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Constrained Optimal Risk Sensitive Execution Problem with Stochastic Market Depth

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