6533b859fe1ef96bd12b7749
RESEARCH PRODUCT
A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets
Ansgar JüngelBertram Düringsubject
Quadratic growthState variableQuadratic equationIncomplete marketsBellman equationMathematical analysisMonotonic functionUniquenessCovarianceQuasilinear PDE quadratic gradient existence and uniqueness of solutions optimal portfolio incomplete marketMathematicsdescription
We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling 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 influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-01-01 | SSRN Electronic Journal |