We consider an optimal consumption - investment problem for financial markets of Black-Scholes 's type with the random coefficients . The existence and uniqueness theorem for the Hamilton-Jacobi-Bellman (HJB) equation is shown. We construct an iterative sequence of functions converging to the solutionof this equation. An optimal convergence rate for this sequence is found and sharp computable upper bounds for the approximation accuracy of the optimal consumption - investment strategies are obtained. It turns out that the optimal  convergence rate in this case is super geometrical, i.e. is more rapid than any geometrical rate .
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation which is a highly non linear partial differential equation (PDE) of the second oder. By using the Feynman - Kac representation we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of the iterative numerical schemes for both the value function and the optimal portfolio. We show, that in this case, the optimal convergence rate is super geometrical, i.e. is more rapid than any geometrical one. We apply our results to a stochastic volatility financial market .
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consumption - investment problem for financial markets of
investment and consumption problem for a
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's type with the random coefficients . The existence and uniqueness theorem for the Hamilton-Jacobi-Bellman
financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman
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is shown. We construct an iterative sequence of functions converging to the solutionof this equation. An
which is a highly non linear partial differential equation (PDE) of the second oder. By using the Feynman - Kac representation we prove uniqueness and smoothness of the solution. Moreover, we study the
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for this sequence is found and sharp computable upper bounds for the approximation accuracy of the optimal consumption - investment strategies are obtained. It turns out that
of the iterative numerical schemes for both the value function and
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portfolio. We show, that in this case, the optimal
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in this case
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rate
one. We apply our results to a stochastic volatility financial market