In this article, we study the set of equivalent (local) martingale measures for financial markets driven by multi-dimensional diffusions. We give conditions for the existence of equivalent (local) martingale measures in terms of existence and uniqueness properties of martingale problems. 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   .
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 no unbounded profit with bounded risk condition holds, while the classicalno free lunch with vanishing risk condition fails .
R
In this article, we study the set of equivalent (local) martingale measures for financial markets driven by multi-dimensional diffusions. We give conditions for the existence of equivalent (local) martingale measures in terms of existence and uniqueness properties of martingale problems. Based on these we
We
R
. As an application, we construct a financial market
for financial markets driven by multi-dimensional time-inhomogeneous diffusions. Our conditions can be used to construct financial markets
R
number of risky assets determines the absence of arbitrage and equals the number of sources of risk
no unbounded profit with bounded risk
A
condition holds, while the classical
A
no free lunch with vanishing risk
A
condition fails