Source: Ann. Appl. Probab.
Volume 9, Number 4
In the framework of continuous-time, Itô processes models for
financial markets, we study the problem of maximizing the probability of an
agent's wealth at time T being no less than the value C of a
contingent claim with expiration 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, developed in utility maximization literature. We then show how
to modify this approach 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 case of different borrowing and lending rates, as well as "large
investor" models. We also provide a number of explicitly solved examples.
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