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# 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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### Determining Hurst exponent of a Brownian motion

I am trying to determine the Hurst exponent of a simple Brownian motion, however, I seem to get a result that differs from 0.5. I am following the instructions given on the Wikipedia-page, and here is ...
841 views

### Risk neutrality correction for Monte Carlo Bootstrapping according to PRIIP regulation for products of category III

The PRIIP (packaged products) regulation prescribes Monte Carlo bootstrapping simulation for calculation of VaR for products of category III (non-linearly leveraged products). The idea is based on ...
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### Distribution of portfolio values with constant spending rate

If your portfolio is invested in an asset that follows a geometric Brownian motion, and you withdraw a constant dollar amount at the beginning of each year, is there an approximate analytical ...
91 views

### Prove the Markov property for the stochastic process $Y^x_t$
Prove the Markov property for the stochastic process $Y^x_t=xe^{at+bW_t}$ Given a function $u(t,x)=\mathbb{E}[f(Y^*_t)]$ with $Y^*_0=x$. For $s<t$ we have $\mathbb{E}[f(Y^*_t)]=u(t-s,Y^*_s)$ by ...