# Tag Info

Accepted

### Why does the Markowitz mean-variance model require the assumption of normality?

it doesn't require normality. What it requires is that the investor's decisions are determined by mean and variance. A normal distribution is determined by mean and variance, so if you assume joint ...
Accepted

### Why is it so rare for finance theory to depart from the normal distribution?

The Geometric Random Walk: The Starting Point Let me begin by being a little more specific. The simplest, yet relatively sound model of asset prices that we have is this one: \begin{equation} ln S(...

### Is there a closed-form solution for the following integral?

Thanks to Gordon's help, we have that \begin{eqnarray*} F=exp\Big\{d + \frac{{c}^2}{2}\Big\}\Big[ \Phi\Big(\Phi^{-1}\Big(1+b\Big)-{c}\Big)- \Phi\Big(\Phi^{-1}\Big(a+b\Big)-{c}\Big)\Big] \end{eqnarray*}...
Accepted

### Show that $(W_t, \int_0^t W_s ds)$ has a normal joint distribution

Note that \begin{align*} \int_0^t W_s ds &= tW_t -\int_0^t sdW_s \tag{1}\\ &= \int_0^t (t-s)dW_s. \end{align*} Then, for $\lambda_1, \lambda_2 \in \mathbb{R}$, \begin{align*} \lambda_1 W_t + \...
Accepted

### Reconciling Two Claims About Volatility Under Fat Tails

I don't think the claim that "Lévy alpha-stable distributions are better descriptors of returns" is universally accepted. While Mandelbrot (and others before him) has correctly identified ...
Accepted

### Quantile normal and lognormal

Quantiles are preserved under monotonic transformations, hence the quantile for $Y$ is simply the exponential of the quantile of $X$, no need for corrections whatsoever (see here for instance). Put ...
Accepted