On Jump Risk of Liquidation in Limit Order Book

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姓名

何威霆(Wei-ting Ho) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(On Jump Risk of Liquidation in Limit Order Book)

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摘要(中)

本研究探討如何利用限價單在其市場中尋求最佳的交易策略。許多文
獻側重於在暫時性和永久性市場衝擊下，交易成本的極小化；而本文主
要針對在期末時間(T)，在有未成交風險下，使投資人資產的期望指數
效用函數極大化。另一方面，考量價格跳躍的風險，本文假設市場價格
服從跳躍擴散模型。作為投資人，最關注的是最佳交易曲線，因此隨機
最佳化控制為本文的主題。本研究使用漢密爾頓-雅可比-貝爾曼方程式，
藉由此方程以及變數變換的技巧，我們解出了控制因子的解析解。最後，
由模擬分析結果可以發現，我們的研究成果的確降低在有價格跳躍假設
下，投資人期末總資產的變異風險。

摘要(英)

We deal with the optimized problem of portfolio liquidation with submitting limit orders into limit order book in this paper. Many other papers focus on minimizing transaction costs arising from permanent and temporary market impact, while we focus on maximizing the expected exponential utility of our P&L profile at a terminal time T. On the other hand, we also consider the price risk of jumps, so jump diffusion model is introduced. As an investor, the optimal trading curve is one thing that we may concern, thus we are now facing a stochastic optimization problem. To achieve our goal, a Hamilton-Jacobi-Bellman equation is solved with a closed-form solution in our result. We also do some numerical examples to interpret how worthy of our work has made. Indeed, we successfully deduce the variation of investor’s final asset under our framework.

關鍵字(中)

★ 隨機最佳化控制
★ 限價單
★ 漢密爾頓-雅可比-貝爾曼方程
★ 跳躍擴散模型

關鍵字(英)

★ stochastic optimal control
★ limit order book
★ Hamilton-Jacobi-Bellman equation (HJB)
★ jump diffusion

論文目次

摘要........................................................i
Abstract...................................................ii
誌謝......................................................iii
List of Figures............................................vi
List of Tables............................................vii
1 Introduction..............................................1
2 Dynamics to the model.....................................6
3 Optimal quotes............................................7
3.1 Objective..............................................7
3.2 Dynamic programming....................................7
3.3 HJB equation...........................................8
4 Special cases............................................12
4.1 Quote with T goes infinity............................12
4.2 Limiting behavior without price risk..................14
4.3 With extremely high liquidation cost..................14
5 Dependence of parameters.................................16
5.1 In market model.......................................16
5.2 Intensity of arrival rate.............................18
5.3 Others................................................20
5.4 Crossover analysis....................................21
6 Simulations..............................................22
6.1 Setup.................................................22
6.2 Simulation results....................................24
7 Conclusion...............................................27
References.................................................29
Appendices.................................................32

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指導教授

傅承德(Cheng-der Fuh)

審核日期

2015-7-29

推文