# Questions tagged [brownian-motion]

In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.

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### Fractional Brownian Motion's Covariance Proof

Let's have the non independent Brownian motion such : $B_{H}(r)=\frac{1}{A(H)} \int_{R}\left[\left\{(r-s)_{+}\right\}^{H-1 / 2}-\left\{(-s)_{+}\right\}^{H-1 / 2}\right] \mathrm{d} B(s), \quad r \in R$ ...
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### Using geometric brownian motion for stock price forecasting [closed]

I am doing a dissertation in finance on a maths degree. I wanted to forecast stock prices using artifcial neural networks but none of my tutors are able to supervise so I'm having to do something else....
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### Expectation of exponential of 3 correlated Brownian Motion

Consider, are correlated Brownian motions with a given I want to calculate the, , I can't think of a way to solve this although I have solved an expectation question with only a single exponential ...
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### Expectation of $\int_0^t \frac{1}{1+W_s^2} \text dW_s$ [duplicate]

I am trying to calculate the expectation of $$\int\limits_0^t \frac{1}{1+W_s^2} \text dW_s,$$ where $(W_t)$ is a Wiener process. I was told that the value of this expectation is zero. Can someone ...
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### Multiple underlying brownian motions

I'm trying to find a way to price a triple product forward with payoff XYZ at time T using risk-neutral pricing. But I don't really have a math background and I have trouble finding a way to account ...
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### Probability of Hitting time of Brownian motion

Let $B =\{ B(t); t \ge 0\}$ be Brownian motion. What is the probability that $B$ hits state one and then state minus one before time one? My take: Let $T_x = \inf \{ t\ge 0 : B(t) = x\}$, the first ...
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### Relationship between risk and return for GBM and riskless bond

Suppose we have $S$, a stock following geometric Brownian motion ($dS_t = S_t (\mu dt + \sigma dZ_t)$ for $Z =$ Brownian motion) and $B$, a zero coupon bond with rate $r$, i.e. $dB_t = rB_t dt$. In ...
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### Estimating constant and local volatility based on passage times

Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift where ...
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### If $W_t$ is standard Brownian motion, what is $\int_0^T W_t \ln(W_t) dW_t$?

If $W_t$ is standard Brownian motion, what is meant by $\int_0^T W_t dW_t$ in finance? Furthermore, what then is the meaning of $\int_0^T W_t \ln(W_t) dW_t$?
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### Simulating artificial asset prices: Random walk vs Brownian motion?

How well can each simulate the real-life behavior of stock prices, and what considerations or (dis-)advantages must we be aware of when deciding to use each: Random walk with drift Random walk ...