= Solution
Write $\mu_t=(\mu_t^{(1)},\ldots,\mu_t^{(d)})^T$ and define the market price of risk
$$
\theta_t=\sigma_t^{-1}(\mu_t-r_t\mathbf1).
$$
It is bounded by hypothesis. The stochastic exponential
$$
Z_t=\exp\left(-\int_0^t\theta_s^T dW_s-\frac12\int_0^t|\theta_s|^2ds\right)
$$
is a true martingale by the <Novikov condition>. Define the equivalent measure $Q$ by $dQ=Z_TdP$. The <Girsanov theorem> makes
$$
W_t^Q=W_t+\int_0^t\theta_sds
$$
a Brownian motion under $Q$. After discounting by the bank account, every risky price has zero drift and is a $Q$-local martingale.
The discounted wealth of an admissible self-financing strategy is a nonnegative local martingale and hence a <supermartingale>. If an arbitrage existed, its zero initial value would imply nonpositive expected terminal discounted wealth under $Q$, while that wealth is nonnegative and positive with positive $Q$-probability. This contradiction proves that the market has no arbitrage; it is the needed direction of the <equivalent local martingale measure> criterion.
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