未知价格变动信息下在线单向交易的数据驱动型策略设计

doi:10.16381/j.cnki.issn1003-207x.2024.2170

Abstract

Abstract:

In practical applications， the problem of online one-way trading is widely encountered in areas， including foreign exchange， inventory procurement， advertising placement， product sale， leasing issues， etc. In the online one-way trading problem， 1 unit of some asset is to be sold in n periods by DM （decision makers） to maximize their returns. At period $i$ ， the DM must instantaneously determine whether to sell and the quantity to sell， solely relying on current price information p_i without any foresight into future prices， p_i+1， p_i+2，…，p_n . Traditional research typically assumes that DM knows the upper and lower bounds or their ratio of price to formulate effective strategy.In order to abandon the assumption that the upper and lower bounds of price changes need to be predicted in advance in the previous research， a new competitive strategy evaluation conception “λ- universal competitive difference” is proposed based on the competitive difference conception （where λ is the risk preference）. From the seller's perspective， the optimal strategy for DM is delved into to successfully sell one unit of an asset in at most k transactions over n time periods， with the objective of maximizing returns. Then an optimal online strategy $O S U C D$ is devised with the upper and lower bounds of price changes given by m and M. Then， it is elucidated that under specific case when $λ = 12$ ， the λ-universal competitive difference degrades into the competitive difference proposed by Wang et al. （2016），the effectiveness of the strategy $O S U C D$ was indirectly proved thereby. Furthermore， $O S U C D$ is upgraded to a data-driven online strategy $D - O S U C D$ that can select appropriate risk preferences $λ ¯ (m, M)$ based on historical data. Simulation data corroborates the robustness of $D - O S U C D$ 's parameter settings. Notably， the DM does not need to anticipate the assumptions of the upper M and lower bounds m of the future price fluctuations in advance， and can instead flexibly set parameters within a reasonable range.Additionally， the data-driven online strategy $D - O S U C D$ is applied， grounded in the λ-universal competitive difference criterion， to the carbon emission trading products of the China Hubei Carbon Emission Exchange （HBEA）， China Beijing Green Exchange （BEA）， and CEEX China Emissions Exchange （GDEA）. These applications further validate the efficacy and robustness of the strategy $D - O S U C D$ . The data-driven online strategy $D - O S U C D$ in this paper can be used to analyze not only online one-way trading but also other online decision-making problems.

Key words: online one-way trading, data-driven strategy, competitive analysis, λ-universal competitive difference, competitive difference

CLC Number:

F224.3

Wenming Zhang,Na Shu. Data-driven Strategy Designing for the Online One-way Trading Without Known Price Variation Information[J]. Chinese Journal of Management Science, 2026, 34(10): 128-139.

Figures/Tables 13

参数	含义	备注
$n$	交易期数	$n$ 已知
$k$	决策者有效交易次数	$k ∈ N$ 且已知 $1 ≤ k ≤ n - 1$
$p i$	第 $i$ 时期的价格，即第 $i$ 个价格	$p i > 0$
$λ$	决策者的风险偏好	$λ ∈ (0,1)$
$α λ$	偏好为 $λ$ 时的泛竞争差	$α λ$ 越小，性能越好
$φ λ, i$	偏好为 $λ$ 时的第 $i$ 个价格阈值	$φ λ, i > 0$
$s λ, i$	偏好为 $λ$ 时的第 $i$ 个价格阈值下策略的交易量	$∑ i = 1 k s λ, i = 1, s λ, i ≥ 0$
$ε$	阈值的一个微小增量	$ε → 0 +$
$N L P λ$	关于风险偏好 $λ$ 的非线性规划问题	无

已知交易期限

n

和交易次数

k

；给定价格变动下限

m

、上限

M

以及风险偏好

λ

①阈值的确定：根据引理2计算

φ λ, 1 *, φ λ, 2 *, ⋯, φ λ, k *

的值，令

φ λ, 0 * = 0

，

φ λ, k + 1 * = M

，则

φ λ, 0 *, φ λ, 1 *, ⋯, φ λ, k + 1 *

为策略的阈值

②具体操作：在时期 $i i = 1,2, ⋯, n - 1$ 获取价格 $p i$ ，则必存在 $j 0 ≤ j ≤ k$ 使得 $p i ∈ φ λ, j *, φ λ, j + 1 *$ （当 $j ≤ k - 1$ ）或 $p i ∈ φ λ, j *, φ λ, j + 1 *$ 中（当 $j = k$ ）。根据历史价格序列 $p 1, p 2, ⋯, p i - 1$ 及 $φ λ, j *$ 的取值，分两种情况讨论（为表述方便，假设 $p 0 = 0$ ）：

情况1： $φ λ, j * > m a x p 1, p 2, ⋯, p i - 1$ 。令卖出数量 $s i = j k - s 1 + s 2 + ⋯ + s i - 1$ ，即保证 $i$ 期结束时，卖出的总数量为 $j k$ （其中， $s 1, s 2, ⋯, s i$ 分别指的是 $O S U C D λ$ 在时期 $1,2, ⋯, i$ 的卖出数量）

情况2： $φ λ, j * ≤ m a x p 1, p 2, ⋯, p i - 1$ 。此时，不卖出，即 $s i = 0$

在最后时期 $n$ ，将所有剩余数量全部卖出

已知交易期限

n

和交易次数

k

以及历史数据

σ H

；给定价格变动下限

m

和上限

M

Step1：取 $λ = 1 i, 2 i, ⋯ i - 1 i, i ∈ 1, + ∞$ ，其中 $i$ 的选取可视实际应用场景而定，显然 $i$ 越大精度越高

Step2：将 $λ$ 的 $i - 1$ 个值所对应的不同泛竞争差最优在线策略 $O S U C D$ 应用到历史交易数据 $σ H$ 中计算出不同 $λ$ 值对应的收益 $O S U C D (σ H)$ ，求得最优偏好 $λ ¯ (m, M) = a r g m a x λ O S U C D (σ H)$

输出：在线策略

D - O S U C D

即为所设计的数据驱动型在线策略

$M j$	$m i$
$M j$	1	2	3	4	5	6	7	8	9	10
20	0.65	0.60	0.56	0.52	0.49	0.47	0.44	0.42	0.41	0.39
21	0.64	0.58	0.54	0.51	0.48	0.45	0.43	0.41	0.40	0.38
22	0.62	0.57	0.53	0.50	0.47	0.44	0.42	0.40	0.38	0.37
23	0.61	0.56	0.52	0.48	0.45	0.43	0.41	0.39	0.37	0.36
24	0.59	0.54	0.50	0.47	0.44	0.41	0.39	0.38	0.36	0.34
25	0.58	0.52	0.48	0.45	0.42	0.40	0.38	0.36	0.34	0.33
26	0.56	0.51	0.46	0.43	0.40	0.38	0.36	0.34	0.33	0.32
27	0.54	0.48	0.44	0.41	0.39	0.36	0.34	0.33	0.31	0.30
28	0.51	0.46	0.42	0.39	0.36	0.34	0.33	0.31	0.30	0.28
29	0.48	0.43	0.40	0.37	0.34	0.32	0.30	0.29	0.28	0.27

$M j$	$m i$
$M j$	1	2	3	4	5	6	7	8	9	10
20	16.07	16.01	15.97	15.95	15.92	15.91	15.90	15.88	15.87	15.87
21	16.08	16.02	15.97	15.95	15.93	15.91	15.90	15.89	15.88	15.87
22	16.08	16.02	15.98	15.95	15.93	15.91	15.90	15.89	15.88	15.87
23	16.08	16.02	15.98	15.95	15.93	15.92	15.90	15.89	15.88	15.87
24	16.09	16.03	15.99	15.96	15.94	15.92	15.91	15.90	15.89	15.88
25	16.09	16.03	15.99	15.96	15.94	15.93	15.91	15.90	15.89	15.88
26	16.10	16.04	16.00	15.97	15.95	15.93	15.92	15.90	15.89	15.89
27	16.10	16.04	16.00	15.97	15.95	15.94	15.92	15.91	15.90	15.89
28	16.11	16.05	16.01	15.98	15.96	15.94	15.93	15.92	15.91	15.90
29	16.12	16.06	16.02	15.99	15.97	15.95	15.94	15.93	15.92	15.91

$μ$	3	4	5	6	7
$C D A$	6.40	6.58	6.76	6.81	6.95
$O S U C D λ ¯ (m, M)$	6.39	6.60	6.84	6.94	7.12

$M j$ $m i$	$λ ¯ (m, M)$				$D - O S U C D (H B E A)$				$D - O S U C D ¯$	实际收益	$R S$ 收益
$M j$ $m i$	20	25	30	35	20	25	30	35	$D - O S U C D ¯$	实际收益	$R S$ 收益
45	0.86	0.85	0.78	0.69	11900.35	11976.84	11900.35	11900.35	12013.89	11620.88	11511.29
50	0.77	0.70	0.63	0.53	12095.63	12018.06	12018.06	12023.76
55	0.67	0.62	0.55	0.45	12083.16	12088.85	12019.15	12012.37
60	0.61	0.56	0.50	0.41	12083.16	12083.16	12083.16	11935.88

M_j $m i$	$λ ¯ (m, M)$				$D - O S U C D (B E A)$				$D - O S U C D ¯$	实际收益	$R S$ 收益
M_j $m i$	60	70	80	90	60	70	80	90	$D - O S U C D ¯$	实际收益	$R S$ 收益
140	0.74	0.71	0.67	0.61	7702.25	7702.71	7702.71	7693.82	7655.67	7474.88	7255.92
150	0.66	0.62	0.60	0.55	7693.82	7693.82	7643.85	7643.85
160	0.64	0.57	0.53	0.50	7606.04	7634.95	7634.95	7656.01
170	0.57	0.54	0.52	0.47	7643.85	7643.85	7597.15	7597.15

M_j $m i$	$λ ¯ (m, M)$				$D - O S U C D (G D E A)$				$D - O S U C D ¯$	实际收益	$R S$ 收益
M_j $m i$	20	25	30	35	20	25	30	35	$D - O S U C D ¯$	实际收益	$R S$ 收益
50	0.81	0.78	0.74	0.67	576.80	576.80	576.87	573.10	569.63	496.55	495.87
55	0.72	0.65	0.59	0.53	569.40	569.40	573.10	569.40
60	0.65	0.61	0.52	0.50	565.70	565.70	569.40	565.70
65	0.63	0.53	0.48	0.43	565.58	565.70	565.70	565.70

References 32

[1]	李平. VUCA条件下的组织韧性：分析框架与实践启示［J］. 清华管理评论， 2020（6）： 72-83.
	Li P. Organizational toughness under the condition of VUCA： Analytical framework and practical enlightenment［J］. Tsinghua Business Review， 2020（6）： 72-83.
[2]	徐维军，胡茂林，张卫国，等. 具有美式看跌期权的单方向在线外汇兑换竞争策略设计［J］. 系统工程理论与实践， 2011， 31（9）： 1635-1644.
	Xu W J， Hu M L， Zhang W G， et al. Competitive strategy design of one-way online trading with American put option［J］. Systems Engineering-Theory & Practice， 2011， 31（9）： 1635-1644.
[3]	Hu H， Zhang W M. Design and analysis of online strategy for the carbon quota trading problem in a data-driven framework based on λ-competitive rate［J］. Computers & Industrial Engineering， 2025， 206： 111186.
[4]	Zhang W， Zhang Y， Cheng Y， et al. An online trading problem with an increasing number of available products［J］. Journal of Combinatorial Optimization， 2022， 44（1）： 518-531.
[5]	章潇月，代文强，周小渝. 价格与需求同时不确定的原材料占线采购问题［J］.管理科学学报，2024，27（6）： 149-158.
	Zhang X Y， Dai W Q， Zhou X Y. Online procurement for raw materials with price and demand uncertainty［J］. Journal of Management Sciences in China， 2024， 27（6）： 149-158.
[6]	Mohr E. Optimal replenishment under price uncertainty［J］. European Journal of Operational Research， 2017， 258（1）： 136-143.
[7]	隋鑫，代文强，王子绮. 两阶段定向展示广告保量鲁棒投放问题［J］. 中国管理科学， 2024， DOI：10.16381/j.cnki.issn1003-207x.2023.1055
	Sui X， Dai W Q， Wang Z Q. Two-stage robust guaranteed delivery in targeted display advertising［J］. Chinese Journal of Management Science， 2024， DOI： 10.16381/j.cnki.issn1003-207x.2023.1055 .
[8]	Salem J， Gupta S. Secretary problems with biased evaluations using partial ordinal information［J］. Management Science， 2024， 70（8）： 5337-5366.
[9]	Correa J， Cristi A， Feuilloley L， et al. The secretary problem with independent sampling［J］. Management Science， 2025， 71（4）： 2778-2801.
[10]	El-Yaniv R， Fiat A， Karp R M， et al. Optimal search and one-way trading online algorithms［J］. Algorithmica， 2001， 30（1）： 101-139.
[11]	Fung S P Y. Optimal online two-way trading with bounded number of transactions［J］. Algorithmica， 2019， 81（11-12）： 4238-4257.
[12]	Simon H A. A behavioral model of rational choice［J］. The Quarterly Journal of Economics， 1955， 69（1）： 99-118.
[13]	Sleator D D， Tarjan R E. Amortized efficiency of list update and paging rules［J］. Communications of the ACM， 1985， 28（2）： 202-208.
[14]	Fujiwara H， Iwama K， Sekiguchi Y. Average-case competitive analyses for one-way trading［J］. Journal of Combinatorial Optimization， 2011， 21（1）： 83-107.
[15]	Zhang Y， Chin F Y L， Lau F C M， et al. Constant competitive algorithms for unbounded one-Way trading under monotone hazard rate［J］. Mathematical Foundations of Computing， 2018， 1（4）： 383-392.
[16]	Mohr E. Optimal search with bounded daily returns［C］//Proceedings of 2014 International Conference on Control，Decision and Information Technologies （CoDIT），Metz， France，November 3-5， IEEE， 2014： 231-235.
[17]	Schwarz M. Lower and upper bounds for the discrete bi-directional preemptive conversion problem with a constant price interval［J］.Algorithms， 2020， 13（2）： 42.
[18]	Zhang W， Xu Y， Zheng F， et al. Optimal algorithms for online time series search and one-way trading with interrelated prices［J］. Journal of Combinatorial Optimization， 2012， 23（2）： 159-166.
[19]	Schroeder P， Dochow R， Schmidt G. Optimal solutions for the online time series search and one-way trading problem with interrelated prices and a profit function［J］. Computers & Industrial Engineering， 2018， 119： 465-471.
[20]	Schroeder P， Kacem I. Optimal solutions for online conversion problems with interrelated prices［J］. Operational Research， 2022， 22（1）： 423-448.
[21]	Chin F Y L， Fu B， Guo J， et al. Competitive algorithms for unbounded one-way trading［J］. Theoretical Computer Science， 2015， 607： 35-48.
[22]	Chin F Y L， Lau F C M， Tan H， et al. Unbounded one-way trading on distributions with monotone hazard rate［C］//Proceedings of 11th International Conference on Combinatorial Optimization and Applications，Shanghai，China，December 16-18，Springer，2017： 439-449.
[23]	王玮，蓝颖杰. 有限交易机会下占线单向交易问题的竞争差分析［J］系统工程理论与实践， 2021， 41（10）： 2476-2487.
	Wang W， Lan Y J. Online one-way trading problem with limited opportunities based on competitive difference analysis［J］. Systems Engineering-Theory & Practice， 2021， 41（10）： 2476-2487.
[24]	Wang W， Lan Y. Robust one-way trading with limited number of transactions and heuristics for fixed transaction costs［J］. International Journal of Production Economics， 2022， 247： 108437.
[25]	张湘玥，张文明. 限制交易次数在线单向交易的固定阈值型策略研究［J］. 中国管理科学， 2024， DOI：10.16381/j.cnki.issn1003-207x.2024.0510 .
	Zhang X Y， Zhang W M. Optimal fixed threshold-based strategy for the online one-way trading with limited number of transactions［J］. Chinese Journal of Management Science，2024，DOI：10.16381/j.cnki.issn1003-207x.2024.0510 .
[26]	Wang W， Wang L， Lan Y， et al. Competitive difference analysis of the one-way trading problem with limited information［J］. European Journal of Operational Research， 2016， 252（3）： 879-887.
[27]	张文明，杜玉禄. 相邻价格相关的在线单向交易问题的数据驱动型策略设计［J］. 中国管理科学， 2025， 33（5）： 26-33.
	Zhang W M， Du Y L. A data-driven strategy for the online one-way trading problem with interrelated prices［J］. Chinese Journal of Management Science， 2025， 33（5）： 26-33.
[28]	Prosad J M， Kapoor S， Sengupta J. Exploring optimism and pessimism in the Indian equity market［J］. Review of Behavioral Finance， 2015， 7（1）： 60-77.
[29]	Wigniolle B. Optimism， pessimism and financial bubbles［J］. Journal of Economic Dynamics and Control， 2014， 41： 188-208.
[30]	Chari V V， Kehoe P J， Mcgrattan E R. Sticky price models of the business cycle： Can the contract multiplier solve the persistence problem？［J］. Econometrica， 2000， 68（5）： 1151-1179.
[31]	Noel M D. Edgeworth price cycles， cost-based pricing， and sticky pricing in retail gasoline markets［J］. Review of Economics and Statistics， 2007， 89（2）： 324-334.
[32]	王梅，周鹏. 碳排放权分配对碳市场成本有效性的影响研究［J］. 管理科学学报， 2020， 23（12）： 1-11.
	Wang M， Zhou P. Assessing the impact of emission permit allocation on the cost effectiveness of carbon market［J］. Journal of Management Sciences in China， 2020， 23（12）： 1-11.

Data-driven Strategy Designing for the Online One-way Trading Without Known Price Variation Information

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