کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10426933 | 908599 | 2005 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
A 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 62, Issue 3, 1 August 2005, Pages 519-544
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 62, Issue 3, 1 August 2005, Pages 519-544
نویسندگان
Bertram Düring, Ansgar Jüngel,