Bertram Düring () (Department of Mathematics and Informatics, University of Mainz) Ansgar Jüngel () (Department of Mathematics and Informatics, University of Mainz)
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We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number
04-01.