Continuous-Time Models

Reinforcement Learning in High-frequency Market Making ArXiv ID: 2407.21025 “View on arXiv” Authors: Unknown Abstract This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in high-frequency financial economics. Different with most existing literature on methodological research about developing various RL methods for market making problem, our work is a pilot to provide the theoretical analysis. We target the effects of sampling frequency, and find an interesting tradeoff between error and complexity of RL algorithm when tweaking the values of the time increment $Δ$ $-$ as $Δ$ becomes smaller, the error will be smaller but the complexity will be larger. We also study the two-player case under the general-sum game framework and establish the convergence of Nash equilibrium to the continuous-time game equilibrium as $Δ\rightarrow0$. The Nash Q-learning algorithm, which is an online multi-agent RL method, is applied to solve the equilibrium. Our theories are not only useful for practitioners to choose the sampling frequency, but also very general and applicable to other high-frequency financial decision making problems, e.g., optimal executions, as long as the time-discretization of a continuous-time markov decision process is adopted. Monte Carlo simulation evidence support all of our theories. ...

Deep Learning for Solving and Estimating Dynamic Macro-Finance Models ArXiv ID: 2305.09783 “View on arXiv” Authors: Unknown Abstract We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of firms and (2) macroeconomic models with financial frictions. Through these applications, we illustrate the advantages of our method: generality, simultaneous solution and estimation, leveraging the state-of-art machine-learning techniques, and handling large state space. The method is versatile and can be applied to a vast variety of problems. ...

Dynamic Models and Structural Estimation in Corporate Finance ArXiv ID: ssrn-2268569 “View on arXiv” Authors: Unknown Abstract We review the last two decades of research in dynamic corporate finance, focusing on capital structure and the financing of investment. We first cover continuou Keywords: Dynamic Corporate Finance, Capital Structure, Investment Financing, Continuous Time Models, Stochastic Processes, Corporate Finance Complexity vs Empirical Score Math Complexity: 8.0/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper is a literature review focused on structural estimation and dynamic models, which inherently involves advanced mathematics and continuous-time frameworks, but it is a theoretical overview rather than a backtest-ready empirical study. flowchart TD A["Research Goal"] -->|Investigate dynamic models<br>in corporate finance| B["Methodology: Continuous-Time<br>Stochastic Processes"] B --> C["Data: Capital Structure<br>& Investment Data"] C --> D["Computational Process:<br>Structural Estimation"] D --> E{"Key Findings"} E --> F["Optimal Dynamic<br>Capital Structure"] E --> G["Financing Constraints<br>& Investment"]

Dynamic Models and Structural Estimation in CorporateFinance ArXiv ID: ssrn-2091854 “View on arXiv” Authors: Unknown Abstract We review the last two decades of research in dynamic corporate finance, focusing on capital structure and the financing of investment. We first cover continuo Keywords: Dynamic Corporate Finance, Capital Structure, Investment Financing, Continuous Time Models, Stochastic Processes, Corporate Finance Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 3.0/10 Quadrant: Lab Rats Why: The paper is a review of advanced theoretical models (continuous-time contingent claims, dynamic optimization) requiring heavy mathematical formalism, but it focuses on model exposition and intuition rather than presenting new data, backtests, or implementation details. flowchart TD A["Research Goal: Review Dynamic Corporate Finance Models"] --> B["Methodology: Continuous-Time Stochastic Processes"] B --> C["Data/Inputs: Firm-level financial data"] B --> D["Computational Processes: Structural Estimation"] C --> D D --> E["Outcome 1: Optimal Capital Structure"] D --> F["Outcome 2: Investment Financing Dynamics"] D --> G["Outcome 3: Macro-Financial Linkages"] E --> H["Key Findings: Models Explain Debt Heterogeneity & Investment Sensitivity"] F --> H G --> H