15 May - Top of the mountain - Who & What?

[daijapan]

Here are ten unsolved problems in algorithmic trading framed within a pure mathematics context:

1. Optimal Execution Problem: Finding a universally optimal strategy for executing large orders that minimizes market impact and balances execution cost and risk.

2. Prediction of Non-stationary Time Series: Developing mathematical models that can accurately predict the behavior of non-stationary financial time series, taking into account abrupt changes and structural breaks.

3. Stochastic Control in High-Frequency Trading: Formulating a comprehensive mathematical framework for stochastic control problems in the context of high-frequency trading, including optimal trading strategies under varying market conditions.

4. Market Microstructure and Order Book Dynamics: Creating a precise mathematical model that accurately describes the dynamics of the limit order book and its impact on price formation and liquidity.

5. Portfolio Optimization with Transaction Costs and Market Impact: Extending the classical portfolio optimization problem to include realistic transaction costs and market impact, and finding closed-form solutions or efficient numerical methods.

6. Risk Management for Complex Derivatives: Developing advanced mathematical models for the risk management of complex financial derivatives, considering extreme market events and tail risks.

7. Arbitrage Opportunities Detection: Formulating a rigorous mathematical framework to detect and exploit arbitrage opportunities in a highly efficient and competitive market environment.

8. Machine Learning and Algorithmic Trading: Theoretical understanding of machine learning models in the context of algorithmic trading, including the robustness, generalization, and overfitting of trading algorithms.

9. Quantifying Market Efficiency and Inefficiency: Creating a mathematical definition and measure of market efficiency and inefficiency that can be empirically tested and used to improve trading strategies.

10. Mathematical Modelling of Market Sentiment: Developing a quantitative model that accurately captures and predicts the impact of market sentiment on price movements and trading volume.

[daijapan]

Here are the profiles of ten researchers along with their key research keywords and relevant arXiv links:

1. Tucker Balch

   • Profile URL: Tucker Balch at J.P. Morgan
   • Research Keywords: Reinforcement Learning, Algorithmic Trading, Market Microstructure, Financial Data
   • ArXiv URL: Research on Reinforcement Learning for Trading

2. Andrew Ng

   • Profile URL: Andrew Ng at Stanford University
   • Research Keywords: Machine Learning, Deep Learning, Financial Modeling, Quantitative Trading
   • ArXiv URL: Deep Reinforcement Learning in Quantitative Trading

3. Lasse Heje Pedersen

   • Profile URL: Lasse Heje Pedersen at Copenhagen Business School
   • Research Keywords: Market Liquidity, Asset Pricing, Risk Management, ESG Investing
   • ArXiv URL: ESG Driven Pairs Algorithm

4. David Easley

   • Profile URL: David Easley at Cornell University
   • Research Keywords: Market Microstructure, Information Economics, Trading Models, Financial Sentiment
   • ArXiv URL: Financial Sentiment Classification for Algorithmic Trading

5. Terrence Hendershott

   • Profile URL: Terrence Hendershott at UC Berkeley
   • Research Keywords: Algorithmic Trading, High-Frequency Trading, Market Impact, Trading Strategies
   • ArXiv URL: Advancing Algorithmic Trading with Deep Q-Network Models

6. Marco Avellaneda

   • Profile URL: Marco Avellaneda at NYU Courant
   • Research Keywords: Stochastic Processes, Quantitative Finance, Option Pricing, Trading Algorithms
   • ArXiv URL: DeepTraderX: Challenging Conventional Trading Strategies

7. Stephen Hoi

   • Profile URL: Stephen Hoi at Singapore Management University
   • Research Keywords: Online Learning, Machine Learning, Financial Analytics, Trading Systems
   • ArXiv URL: Algorithmic Trading Guided Market Simulation

8. Robert Almgren

   • Profile URL: Robert Almgren at Quantitative Brokers
   • Research Keywords: Optimal Execution, Transaction Cost Analysis, Quantitative Trading, Financial Engineering
   • ArXiv URL: Optimal Execution and Market Microstructure

9. Michael Kearns

   • Profile URL: Michael Kearns at University of Pennsylvania
   • Research Keywords: Machine Learning, Algorithmic Trading, Privacy in AI, Financial Models
   • ArXiv URL: Deep Reinforcement Learning in Financial Markets

10. Matthew Dixon

    • Profile URL: Matthew Dixon at Illinois Tech
    • Research Keywords: Stochastic Calculus, Financial Modeling, Machine Learning, Algorithmic Trading
    • ArXiv URL: Interactive Agent-Guided Simulation for Trading

These researchers are leading advancements in their respective fields, contributing to the development and refinement of algorithmic trading techniques through their rigorous research and innovative approaches.