Existence of solutions for the nonlinear partial differential equation arising in the optimal investment problem. (English) Zbl 1139.35059

Summary: We are concerned with the solvablity of certain nonlinear partial differential equation, 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.


35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
91B28 Finance etc. (MSC2000)
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI Euclid


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