Abstract
This paper addresses the problem of choosing the optimum portfolio in the context of continuous time jump stochastic models. The aim is to maximize the wealth of a small risk-averse investor that operates in this financial market. When the case of complete observation is considered, the optimal control problem is formulated and the Hamilton-Jacobi-Bellman equation is solved to yield the solution. On the other hand, to deal with the case of partial observation, the filter equations of the non-observed process are calculated and a sub-optimal control law is presented.
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