Nonlinear Dynamics in Economics: From Chaos Theory to Reinforcement Learning and Market Forecasts

Morning (Lectures)

• Qualitative theory of smooth one-dimensional discrete-time dynamical systems
• Fixed points, stability, bifurcations, and local and global dynamics
• Non-smooth maps: piecewise-smooth functions, discontinuities, border-collision bifurcations, and coexistence of attractors
• Period-doubling cascades, periodic orbits, and routes to chaos.

Afternoon (Applications and labs)

• Simple behavioral trading rules and nonlinear price adjustment mechanisms
• Commodity and financial market models with trend-following and contrarian strategies
• Numerical exploration of bifurcation diagrams, basins of attraction, and Lyapunov exponents

Morning (Lectures)

• Qualitative theory of smooth and non-smooth two-dimensional discrete-time systems
• Fixed points, eigenvalues, stability, and local bifurcationsInvariant manifolds, periodic orbits, attractors, and basin geometry
• Non-smooth bifurcations, multistability, and the emergence of complex dynamics

Afternoon (Applications and labs)

• Two-dimensional exchange-rate models incorporating expectations and feedback mechanisms
• Interactions between fundamentalist and chartist traders in foreign exchange (FX) markets
• Numerical analysis of phase portraits, attractors, stability regions, and parameter-dependent transitions

Morning (Lectures)

• Nonlinear models of interest rates, oil prices, and financial markets
• Model calibration and parameter estimation for nonlinear and non-smooth systems
• Time-series analysis and the identification of periodic, aperiodic, and chaotic dynamics
• Financial stylized facts: volatility clustering, heavy-tailed returns, nonlinear dependence, and regime changes
• Model validation, parameter uncertainty, and the limitations of empirical identification

Afternoon (Applications and labs)

• Simulating and estimating selected nonlinear models for interest rates, oil prices, and financial markets
• Comparing simulated and observed time series
• Assessing whether estimated models reproduce key statistical properties of market data

Morning (Lectures)

• Foundations of reinforcement learning: states, actions, rewards, and policies
• Q-learning and Deep Q-Networks (DQN)
• Trading agents in nonlinear and non-stationary market environments
• Endogenous changes in market dynamics and their implications for learning and profitability
• Benchmarking and out-of-sample evaluation of reinforcement learning strategies
• Afternoon (Applications and labs)
• Implementing a DQN trading agent in a simulated market
• Comparing its performance with a market without a learning agent, random trading policies, and fixed strategies
• Evaluating profitability, robustness, and sensitivity to changing market conditions

Morning (Lectures)

• Integrating exogenous information into nonlinear market models
• Introduction to convolutional neural networks (CNNs) for extracting features from satellite imagery
• Satellite-derived indicators for commodity and energy markets
• Hybrid approaches combining nonlinear dynamical systems, market data, and machine learning
• Out-of-sample forecasting, benchmark selection, and predictive performance evaluation

Afternoon (Applications and labs)

• Constructing a forecasting exercise using market data and additional indicators, such as satellite-derived measures
• Comparing a baseline nonlinear model with an information-enriched specification
• Evaluating predictive gains and examining whether additional information helps characterize market dynamics
• Final discussion of results, limitations, and possible extensions