In this paper, we study a weak notion of viability for a controlled diffusion. Under a tangential hypothesis, we prove that the weak viability property is satisfied.

We consider the portfolio problem in continuous-time where the objective of the investor or money manager is to exceed the performance of a given stochastic benchmark, as is often the case in institutional money management. The benchmark is driven by a stochastic process that need not be...

Suppose that L=[summation operator]i, j=1daij(x)[not partial differential]2/[not partial differential]xi[not partial differential]xj is uniformly elliptic. We use XL(t) to denote the diffusion associated with L. In this paper we show that, if the dimension of the set is strictly less than d, the...