chore: new list

Author: DiogoRibeiro7

_posts/-_ideas/math_topics_macroeconomics.md

@@ -0,0 +1,57 @@
+## TODO: Mathematical Topics in Macroeconomics
+
+### 1. **TODO: Mathematical Foundations of Macroeconomic Models**
+   - **TODO: Differential Equations in Growth Models**: Examine how differential equations are used to model economic growth, especially in models like the **Solow Growth Model** or **Romer’s Endogenous Growth Model**.
+   - **TODO: Dynamic Systems in Economics**: Discuss how dynamic systems theory is applied to macroeconomics to understand changes over time.
+   - **TODO: Optimal Control Theory in Economics**: Explore the use of Hamiltonian and Lagrangian techniques in models of fiscal and monetary policy.
+
+### 2. **TODO: Stochastic Processes and Uncertainty in Macroeconomics**
+   - **TODO: Stochastic Differential Equations (SDEs)**: Explain how SDEs model uncertainty in macroeconomic variables like inflation, interest rates, and exchange rates.
+   - **TODO: Markov Chains and Markov Decision Processes**: Discuss the role of Markov models in **Real Business Cycle (RBC)** and **Dynamic Stochastic General Equilibrium (DSGE)** models.
+
+### 3. **TODO: Econometrics and Mathematical Statistics in Macroeconomics**
+   - **TODO: Time Series Analysis**: Dive into ARIMA models, Vector Autoregressions (VAR), and cointegration analysis.
+   - **TODO: Bayesian Econometrics**: Discuss Bayesian inference and techniques like **Markov Chain Monte Carlo (MCMC)** in macroeconomic problems.
+
+### 4. **TODO: Game Theory in Macroeconomic Policy**
+   - **TODO: Nash Equilibrium and Macroeconomic Policy**: Explain the application of Nash equilibrium in monetary and fiscal policy interactions.
+   - **TODO: Repeated Games and Economic Cooperation**: Analyze international trade negotiations or currency wars using repeated game theory.
+
+### 5. **TODO: Mathematical Models of Inflation and Interest Rates**
+   - **TODO: Phillips Curve**: Explore the mathematical representation of the Phillips curve, relating inflation to unemployment.
+   - **TODO: Term Structure of Interest Rates**: Discuss the **Vasicek** and **Cox-Ingersoll-Ross (CIR)** models for interest rate dynamics.
+
+### 6. **TODO: Macroeconomic Optimization Problems**
+   - **TODO: Dynamic Optimization in Macroeconomics**: Explore Bellman equations and dynamic programming in consumption and investment models.
+   - **TODO: Overlapping Generations Models (OLG)**: Use OLG models to study long-term trends in debt and wealth distribution.
+
+### 7. **TODO: Monetary and Fiscal Policy: A Mathematical Perspective**
+   - **TODO: Taylor Rule and Monetary Policy**: Introduce the mathematical formulation of the Taylor rule.
+   - **TODO: Debt Dynamics and Fiscal Sustainability**: Use differential equations to model government debt over time.
+
+### 8. **TODO: Mathematical Models of Labor Markets**
+   - **TODO: Search and Matching Models**: Explore the **Diamond-Mortensen-Pissarides (DMP) model** in labor economics.
+   - **TODO: Wage Dynamics and Bargaining Models**: Introduce the Nash Bargaining Solution and its applications to wage negotiations.
+
+### 9. **TODO: International Economics and Mathematical Models**
+   - **TODO: Exchange Rate Models**: Introduce models like **Purchasing Power Parity (PPP)** and **Uncovered Interest Parity (UIP)**.
+   - **TODO: Optimal Currency Areas (OCA)**: Analyze the mathematical conditions for an optimal currency area.
+
+### 10. **TODO: Computational Macroeconomics and Numerical Methods**
+   - **TODO: Solving DSGE Models Numerically**: Discuss methods like **perturbation techniques** and **finite difference methods** for solving DSGE models.
+   - **TODO: Monte Carlo Simulations**: Explore the use of Monte Carlo methods in macroeconomic simulations.
+
+### 11. **TODO: Inequality and Growth: Mathematical Models**
+   - **TODO: Solow Growth Model and Extensions**: Extend the Solow model to include technological change and human capital.
+   - **TODO: Mathematical Models of Inequality**: Use **Lorenz curves** and **Gini coefficients** to measure economic inequality.
+
+### 12. **TODO: Chaos Theory and Nonlinear Dynamics in Macroeconomics**
+   - **TODO: Chaos and Economic Cycles**: Explore chaotic dynamics and bifurcation theory in macroeconomic cycles.
+   - **TODO: Nonlinear Growth Models**: Discuss the role of non-linearities in macroeconomic growth models.
+
+### 13. **TODO: Behavioral Macroeconomics and Agent-Based Modeling**
+   - **TODO: Mathematics of Behavioral Biases**: Introduce mathematical models of behavioral biases such as loss aversion.
+   - **TODO: Agent-Based Models (ABM)**: Explore agent-based modeling and its mathematical foundations in macroeconomics.
+
+### TODO: Final Thoughts
+These topics combine macroeconomics and mathematics, showing how mathematical tools are essential for developing, analyzing, and solving complex macroeconomic models.