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Assuming the basic VE line on knowledge is correct, we get an elegant solution to the value problem.
In this paper, we have used a neural network to obtain an approximate solution to the value function of the HJB (Hamilton Jacobi Bellman) equation.
At each age we solve the value function and optimal policy rule, given the current state variables and the solution to the value function in the next period.
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We prove convergence of the approximate solutions to the value function of the original problem, by using the uniqueness result for viscosity solutions.
Complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries.
The exponential function on, defined by (2.1). is the solution to the initial value problem.
The solution to the initial value problem (11) is, see [18] (12).
Let, satisfying in, be the unique solution to the boundary value problems (3.2). respectively, where (3.3).
Next, we prove the existence and uniqueness of a solution to the initial value problem (4.7).
Suppose that is a smooth positive solution to the boundary value problem (1.1) and (1.2).
To establish the existence of a solution to the boundary value problem (1.1), we need to make the following assumptions.
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