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Our goal is to analyze the system of Hamilton-Jacobi-Bellman equationsarising in derivative securities pricing models. The European style of anoption price is constructed as a difference of the certainty equivalents to thevalue functions solving the system of HJB equations. We introduce thetransformation method for solving the penalized nonlinear partial differentialequation. The transformed equation involves possibly non-constant the riskaversion function containing the negative ratio between the second and firstderivatives of the utility function. Using comparison principles we deriveuseful bounds on the option price. We also propose a finite differencenumerical discretization scheme with some computational examples.

Utility indifference Option Pricing Model with a Non-Constant Risk-Aversion under Transaction Costs and Its Numerical Approximation