A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets - Bertram Düring; Ansgar Jüngel (University of Konstanz, Center of Finance and Econometrics (CoFE), 2004)
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 in uence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
urn:nbn:de:bsz:352-opus-11686
Keywords: 330; Quasilinear PDE; quadratic gradient; existence and uniqueness of solutions; optimal portfolio; incomplete market; Portfolio-Management; Mathematische Optimierung; Finanzmarkt; Unvollkommener Markt; Erwartungsnutzen; Theorie