A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

No 04-01, CoFE Discussion Paper from Center of Finance and Econometrics, University of Konstanz

Abstract: 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.

Keywords: Quasilinear PDE; quadratic gradient; existence and uniqueness of solutions; optimal portfolio; incomplete market (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fin and nep-fmk
Date: 2004-01

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