Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem
Abe, Ryo ; Ishimura, Naoyuki
Proc. Japan Acad. Ser. A Math. Sci., Tome 84 (2008) no. 1, p. 11-14 / Harvested from Project Euclid
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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.
Publié le : 2008-01-15
Classification:  Absolute risk aversion,  nonlinear partial differential equations,  solvability,  35K60,  91B28; 91B30 
@article{1201186679,
     author = {Abe, Ryo and Ishimura, Naoyuki},
     title = {Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {84},
     number = {1},
     year = {2008},
     pages = { 11-14},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1201186679}
}

Abe, Ryo; Ishimura, Naoyuki. Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem. Proc. Japan Acad. Ser. A Math. Sci., Tome 84 (2008) no. 1, pp.  11-14. http://gdmltest.u-ga.fr/item/1201186679/