b. kafash∗
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In this paper, the stochastic optimal control problems, which frequently occur in economic and finance are investigated. First, using Bellman’s dynamic programming method the stochastic optimal control problems are converted to Hamilton-Jacobi-Bellman (HJB) equation. Then, obtained HJB equation is solved through the method of separation of variables by guessing a solution via its terminal condition. Also, the non-linear optimal feedback control law is constructed. Finally, the solution procedure is illustrated for solving some examples that two of them are financial models. In fact, to highlight the applications of stochastic optimal control problems in financial mathematics, some financial models are presented.
Keywords: Phrases: Stochastic optimal control problems, Hamilton-Jacobi-Bellman (HJB) equations, financial applications, method of separation of variablES -
In this paper, it is attempted to approximate the real and complex roots of nonlinear equations. For this reason, by considering the convergence conditions of Adomian decomposition method for solving functional equations, a new appropriate method is presented. It will be shown that the proposed method can be computed suitable approximate real and complex roots of a given function more efficient than Maple software. Furthermore, with providing some examples the aforementioned cases are dealt with numerically.
Keywords: Complex solution of nonlinear equations, Adomian decomposition method (ADM), convergence conditions of ADM, Banach’s fixed point theorem
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