 Singular initial market-price-of-risk obstruction

A positive normalized continuous local martingale deflator requires a locally square-integrable Brownian diffusion coefficient. If the forced market price of risk is $-t^{-1/2}$, the coefficient has magnitude $Z_t/\sqrt{t}$. Since $Z_0>0$, continuity makes its squared integral diverge near zero. The bank account can nevertheless exist because $t^{-1/2}$ itself is integrable; finite integrated interest is weaker than square-integrability of the required risk compensation.