= Bounded-coefficient asset deflator
{title2=$d(Z_tS_t^i)=Z_tS_t^i(\sigma_{t,i}-\lambda_t)^T\,dW_t$}
For asset dynamics $dS=\operatorname{diag}(S)(\mu\,dt+\sigma\,dW)$, let $\lambda=\sigma^{-1}\mu$ and $Z=\mathcal E(-\int\lambda^T\,dW)$. The <Itô product rule> cancels the drift of each $ZS^i$, leaving the displayed <stochastic integral>. When $\mu$ is bounded and $\sigma\sigma^T\geq\varepsilon I$, $\lambda$ is bounded and the <Novikov condition> makes $Z$ a true <martingale> on every finite horizon. If $\sigma$ is also bounded, each $ZS^i/S_0^i$ satisfies the <Novikov condition> as a <stochastic exponential> with bounded integrand $\sigma_i-\lambda$, so it too is a true <martingale>.
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