# Irrelevance of Capital Structures with Complete Markets

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

from scipy.stats import norm

from numba import njit, prange

from quantecon.optimize import root_finding

%matplotlib inline

```

```{code-cell} python3

# Equilibrium Capital Structures with Incomplete Markets

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython3

```{index} single: Models; Additive functionals

```

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython3

import scipy.linalg as la

import quantecon as qe

import matplotlib.pyplot as plt

%matplotlib inline

from scipy.stats import norm, lognorm

```

# Optimal Taxation without State-Contingent Debt

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

# Fluctuating Interest Rates Deliver Fiscal Insurance

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

```{code-cell} ipython

import matplotlib.pyplot as plt

%matplotlib inline

from scipy.optimize import fsolve, fmin

```

# Fiscal Risk and Government Debt

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

```{code-cell} ipython

import matplotlib.pyplot as plt

%matplotlib inline

from scipy.optimize import minimize

```

# Default Risk and Income Fluctuations

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} python

import matplotlib.pyplot as plt

import numpy as np

import quantecon as qe

from numba import njit, prange

%matplotlib inline

```

## Structure

# {index}`Covariance Stationary Processes <single: Covariance Stationary Processes>`

```{contents} Contents

:depth: 2

```

In addition to what's in Anaconda, this lecture will need the following libraries:

```{code-cell} ipython

```{code-cell} ipython

import numpy as np

import matplotlib.pyplot as plt

%matplotlib inline

import quantecon as qe

```

```{index} single: Elementary Asset Pricing

```

```{contents} Contents

:depth: 2

```

## Overview

This lecture is about some implications of asset-pricing theories that are based on the equation

```{code-cell} ipython3

import matplotlib.pyplot as plt

import numpy as np

%matplotlib inline

# Define the function to plot

def y(x, alpha, beta):

import numpy as np

import statsmodels.api as sm

import matplotlib.pyplot as plt

%matplotlib inline

```

Lots of our calculations will involve computing population and sample OLS regressions.

# Two Modifications of Mean-Variance Portfolio Theory

```{contents} Contents

:depth: 2

```

## Overview

This lecture describes extensions to the classical mean-variance portfolio theory summarized in our lecture [Elementary Asset Pricing Theory](https://python-advanced.quantecon.org/asset_pricing_lph.html).

import numpy as np

import scipy.stats as stat

import matplotlib.pyplot as plt

%matplotlib inline

from ipywidgets import interact, FloatSlider

```