Before revision:  Based on these we derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures . As an application, we construct a financial market in which the number of risky assets determines the absence of arbitrage and equals the number of sources of risk   .
After revision:  Based on these we derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets in which the number of risky assets determines the absence of arbitrage and equals the number of sources of risk .