# Questions tagged [normal-distribution]

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### Necessary conditions to ensure that stochastic integral is a normal variable

Let $\left(W_t\right)_{t\geq 0}$ be a Brownian motion with respect to filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\geq 0}$. Let $\left(\alpha_t\right)_{t\geq 0}$ be an $\mathbb{F}$-adapted ...
55 views

### Distribution of discrete Geometric average and Stock Price

If we have $$S_t = S_0 e^{(r-\frac{1}{2} \sigma ^2) +\sigma W_t}$$ and a discrete geometric average of stock prices $$G_n = (\prod_{i=1}^{n} S_{t_i})^{\frac{1}{n}}$$ where the monitoring points are ...
79 views

### Why don’t methods focus on constructing expected distributions and solving the integrals

Everyone knows assumptions of normality etc are bad and that the expected distributions of financial quantities (such as returns) change depending on the circumstances. We know that we can compute the ...
292 views

### Kelly Criterion for cash game poker (normally distributed returns)

I'm trying to apply the Kelly Criterion to poker. Poker players have been stuck using outdated bankroll management techniques for decades, and I want to change that. My goal is to graph the log growth ...
1 vote
108 views

### How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions?

I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am ...
70 views

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### Central limit theorem and normality assumption of asset return distribution

Can central theorem justify normality assumption of assets return distribution? And if it can why the empirical evidence show this assumption, which many finance models are based on, is a far cry from ...
1 vote
231 views

### Price is Log-normal distributed, yet the return is non-normal

I have a price series. The natural logarithm of the price shows good normality. As shown in the standardized normal probability plot below: However, by viewing the standardized normal probability ...
476 views

### Log normal price simulation

I'm trying to figure out a spreadsheet I have which simulates 50000 returns in excel using the following function: LOGNORM.INV(RAND(),0,0.35)-1 Question: How ...
71 views

### Quantile with periodic investing

Short Version Can I get a quantile of such an expression? \begin{equation} \sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma))) \end{equation} I know I can do it for one part of ...
Let's assume we have a normal distribution $X\sim \mathcal{N}(\mu,\sigma^2)$. In a normal distribution the quantile can be calculated as follows: \begin{equation} \Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {...