File(s) not publicly available
Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets
journal contribution
posted on 2023-06-07, 23:09 authored by Bertram Duering, Ansgar JüngelA quasilinear parabolic equation with quadratic gradient terms is analyzed. The equation models an optimal portfolio in so-called incomplete financial markets consisting of risky assets and non-tradable state variables. Its solution allows to compute an optimal portfolio strategy. The quadratic gradient terms are essentially connected to the assumption that the so-called relative risk aversion function is not logarithmic. The existence of weak global-in-time solutions in any dimension is shown under natural hypotheses. The proof is based on the monotonicity method of Frehse. Furthermore, the uniqueness of solutions is shown under a smallness condition on the derivatives of the covariance (¿diffusion¿) matrices using a nonlinear test function technique developed by Barles and Murat. Finally, the influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example in three dimensions.
History
Publication status
- Published
Journal
Nonlinear AnalysisExternal DOI
Issue
3Volume
62Page range
519-544Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC