= Solution
The cash-discounted stock is a positive <continuous local martingale>, because its dynamics contain no drift. Applying <Itô formula> to $\pi_t=U(t,v_t,S_t)$, the displayed partial differential equation cancels its drift exactly, leaving another local martingale. Since $U$ is bounded, $\pi$ is in fact a true martingale.
Thus the physical measure itself is an <equivalent local martingale measure> relative to cash for all three traded assets. The continuous-time <fundamental theorem of asset pricing> rules out arbitrage, more precisely no free lunch with vanishing risk, in the usual admissible class.
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