Maximizing the probability of a perfect hedge

In the framework of continuous-time, Ito processes models for financial mar kets, we study the problem of maximizing the probability of an agent's weal th at time T being no less than the value C of a contingent claim with expi ration time T. The solution to the problem has been known in the context of complete markets and recently also for incomplete markets; we rederive the complete markets solution using a powerful and simple duality method, deve loped in utility maximization literature. We then show how to modify this a pproach to solve the problem in a market with partial information, the one in which we have only a prior distribution on the vector of return rates of the risky assets. Finally, the same problem is solved in markets in which the wealth process of the agent has a nonlinear drift. These include the ca se of different borrowing and lending rates, as well as "large investor" mo dels. We also provide a number of explicitly solved examples.