Optimization of dynamic portfolio under model uncertainty

The problem of optimal portfolio under model uncertainty and a general semimartingale market was studied. First, a solution to the investment problem was obtained using the martingale method and the dual theory. It was proven that under appropriate assumptions a unique solution to the investment problem exists and is characterized. Then, the value functions of the primal and dual problem are convex conjugate functions. Finally, a diffusion-jump-model was considered where the coefficients depend on the state of a Markov chain and the investor is uncertain about the intensity of the underlying Poisson process. For an agent with logarithmic utility function, the stochastic control method was adopted to derive the Hamilton-Jacobi-Bellmann-equation. Furthermore, the solution of the dual problem can be determined and it was shown how the optimal portfolio can be explicitly computed.