= Arithmetic stock model with constant volatility
{title2=$dS_t=\mu\,dt+\sigma\,dW_t$}
= Arithmetic Brownian stock model
{synonym}
This additive price model has constant absolute volatility and can take negative <stock> values. With constant cash interest rate $r$, its <market price of risk> is $(\mu-rS_t)/\sigma$. Under an equivalent <risk-neutral measure>, its drift becomes $rS_t$, so its conditional law is <Gaussian> with mean $e^{r(T-t)}S_t$ and <variance> $\sigma^2(e^{2r(T-t)}-1)/(2r)$. It is distinct from a multiplicative Black–Scholes diffusion.
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