Table of Links Abstract Abstract Abstract Introduction
1.1 Periodic auction and continuous limit order book
1.2 Comparison and main flaws of limit order book
1.3 Optimal policies to cure auction’s inefficiencies and related works


Auctions market modeling with transaction fees and randomization
2.1 The market characteristics
2.2 Clearing Price rule
2.3 Strategic Trader’s optimization and market quality
2.4 Data and numerical analysis
2.5 Strategic trader with full information: efficient but unfair market
2.6 Imperfect information and inefficiency of auctions


Monitoring policies: transaction fees and clearing time randomization
3.1 Bilevel optimization between the exchange and the strategic trader
3.2 Randomization without fees
3.3 Optimal transaction fees indexed on time to improve price impact for the trader
3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees


Conclusions Introduction
1.1 Periodic auction and continuous limit order book
1.2 Comparison and main flaws of limit order book
1.3 Optimal policies to cure auction’s inefficiencies and related works Introduction Introduction 1.1 Periodic auction and continuous limit order book 1.1 Periodic auction and continuous limit order book 1.2 Comparison and main flaws of limit order book 1.2 Comparison and main flaws of limit order book 1.3 Optimal policies to cure auction’s inefficiencies and related works 1.3 Optimal policies to cure auction’s inefficiencies and related works Auctions market modeling with transaction fees and randomization
2.1 The market characteristics
2.2 Clearing Price rule
2.3 Strategic Trader’s optimization and market quality
2.4 Data and numerical analysis
2.5 Strategic trader with full information: efficient but unfair market
2.6 Imperfect information and inefficiency of auctions Auctions market modeling with transaction fees and randomization Auctions market modeling with transaction fees and randomization 2.1 The market characteristics 2.1 The market characteristics 2.2 Clearing Price rule 2.2 Clearing Price rule 2.3 Strategic Trader’s optimization and market quality 2.3 Strategic Trader’s optimization and market quality 2.4 Data and numerical analysis 2.4 Data and numerical analysis 2.5 Strategic trader with full information: efficient but unfair market 2.5 Strategic trader with full information: efficient but unfair market 2.6 Imperfect information and inefficiency of auctions 2.6 Imperfect information and inefficiency of auctions Monitoring policies: transaction fees and clearing time randomization
3.1 Bilevel optimization between the exchange and the strategic trader
3.2 Randomization without fees
3.3 Optimal transaction fees indexed on time to improve price impact for the trader
3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees Monitoring policies: transaction fees and clearing time randomization Monitoring policies: transaction fees and clearing time randomization 3.1 Bilevel optimization between the exchange and the strategic trader 3.1 Bilevel optimization between the exchange and the strategic trader 3.2 Randomization without fees 3.2 Randomization without fees 3.3 Optimal transaction fees indexed on time to improve price impact for the trader 3.3 Optimal transaction fees indexed on time to improve price impact for the trader 3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees 3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees Conclusions Conclusions Conclusions Conclusions A. Appendix: Numerical Methods A. Appendix: Numerical Methods A.1 Problem of a Strategic Seller A.1 Problem of a Strategic Seller A.2 Appendix: Problem of the Regulator A.2 Appendix: Problem of the Regulator B Appendix: Illustrate Remark 2.4 B Appendix: Illustrate Remark 2.4 References References 3.1 Bilevel optimization between the exchange and the strategic trader where[8] Remark 3.1. This problem can by also seen as a “trader focused” exchange. We assume the exchange wants to minimize the total spread for the trader, where Remark 3.1. This problem can by also seen as a “trader focused” exchange. We assume the exchange wants to minimize the total spread for the trader, where total spread =MQ + transaction spread total spread =MQ + transaction spread = spread between efficient price and clearing price+ = spread between efficient price and clearing price+ spread between clearing price and after-fee price (real executed price). spread between clearing price and after-fee price (real executed price). If the exchange focuses only on the market efficiency and wants to increase both fee gains and market quality, the problem becomes Remark 3.2. Note that for both market impact or market efficiency optimization problems, we focus solely on the spread and fee of the strategic trader. We do not include the spread and fee of the other transferred limit orders because we assume these traders are transferred from CLOB to the periodic auction for execution and thus do not face the transaction fee imposed in the periodic auction. Remark 3.2. Note that for both market impact or market efficiency optimization problems, we focus solely on the spread and fee of the strategic trader. We do not include the spread and fee of the other transferred limit orders because we assume these traders are transferred from CLOB to the periodic auction for execution and thus do not face the transaction fee imposed in the periodic auction. 3.2 Randomization without fees 3.3 Optimal transaction fees indexed on time to improve price impact for the trader We now turn to a deeper study of how our transaction fee model improves the market’s quality for the Apple’s stock price.[9] Both the linear transaction fee structure and square transaction fee structure encourage the strategic seller to arrive earlier in the market. From Figure 3 (a) and (b), we see that as the fee increases (led by increasing a), the strategic seller’s optimal τ gradually declines from 10 to 1 and the decline rate seems to coincide with the structure of the fee model as Figure 3 (a) shows a linear declining pattern and Figure 3 (b) shows an accelerating declining pattern. 3.4 Optimal transaction fees indexed on time: improving market quality while benefiting from the fees We now turn to the solutions of (3.5) and (3.6). The bilevel optimization problem thus becomes Remark 3.3. In an informal way, we can see from (3.9) or (3.10) that Remark 3.3. In an informal way, we can see from (3.9) or (3.10) that Exchange value function = market quality cost − fees, Exchange value function = market quality cost − fees, or in other words or in other words Market quality cost = Exchange gain + Fees’ gain. Market quality cost = Exchange gain + Fees’ gain. Authors:
(1) Thibaut Mastrolia, UC Berkeley, Department of Industrial Engineering and Operations Research (thibaut.mastrolia@berkeley.edu);
(2) Tianrui Xu, UC Berkeley, Department of Mathematics (tianrui.xu@berkeley.edu). Authors: Authors: (1) Thibaut Mastrolia, UC Berkeley, Department of Industrial Engineering and Operations Research (thibaut.mastrolia@berkeley.edu); (2) Tianrui Xu, UC Berkeley, Department of Mathematics (tianrui.xu@berkeley.edu). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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