Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem

被引：13

作者：

Abe, Ryo ^{[1
]}

Ishimura, Naoyuki ^{[2
]}

机构：

[1] Simplex Technol Inc, Tokyo 1030027, Japan

[2] Hitotsubashi Univ, Grad Sch Econ, Dept Math, Kunitachi, Tokyo 1868601, Japan

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2008年 / 84卷 / 01期

关键词：

absolute risk aversion; nonlinear partial differential equations; solvability;

D O I：

10.3792/pjaa.84.11

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with the solvablity of certain nonlinear partial differential equation (PDE), which is derived from the optimal investment problem under the random risk process. The equation describes the evolution of the Arrow-Pratt coefficient of absolute risk aversion with respect to the optimal value function. Employing the fixed point approach combined with the convergence argument we show the existence of solutions.

引用

页码：11 / 14

页数：4

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