توجه: محتویات این صفحه به صورت خودکار پردازش شده و مقاله‌های نویسندگانی با تشابه اسمی، همگی در بخش یکسان نمایش داده می‌شوند.
۱Solution of Optimal Control Problems by Modified State Parameterization
اطلاعات انتشار: کنفرانس بین المللی مدل سازی غیر خطی و بهینه سازی، سال
تعداد صفحات: ۷
In this paper a new parameterization is introduced by Boubaker polynomials, which can accurately represent state variable with only a few parameters.In fact, an efficient algorithm forsolving optimal control problems and the controlled linear and Duffing oscillator is presented. This algorithm converts these problems to a non–linear optimization problem. By this method, the control and state variables can be approximated as a function of time. Also, the numerical value of the performance index is obtained readily. Convergence of the algorithms is proved and someillustrative examples are presented to show the efficiency and reliability of the presented method<\div>

۲American Options Pricing by Using Stochastic Optimal Control Problems
نویسنده(ها): ، ،
اطلاعات انتشار: سومین کنفرانس ریاضیات مالی و کاربردها، سال
تعداد صفحات: ۵
Stochastic optimal control problems frequently occur in Economics and Finance. Dynamicprogramming method represents the most known method for solving optimal control prob–lems analytically. As analytical solutions for problems of optimal control are not alwaysavailable, finding an approximate solution is at least the most logical way to solve them.In this paper, we present some of the basic ideas which are in current use for the solutionof the dynamic programming equations. Also, based on the Markov chain approximationtechniques, a numerical procedure is constructed for solution of stochastic optimal controlproblems. We focus on the approximation in value space method. And the Jacobi andGauss–Seidel relaxation (iterative) methods are discussed. These are fundamental iterativemethods which are used in value space approach. Finally, American options pricing arepresented as simplest control problem which is called optimal stopping problem.<\div>

۳Portfolio optimization problem with default risk
نویسنده(ها): ، ،
اطلاعات انتشار: سومین کنفرانس ریاضیات مالی و کاربردها، سال
تعداد صفحات: ۶
In this paper, we consider a stochastic portfolio optimization problem with default risk on an infinite time horizon. An investor dynamically chooses a consumption rate and allocates the wealth into the securities: a perpetual defaultable bond, a money market account with the constant return and a default–free risky asset. The goal is to choose the optimal investment to maximize the infinite horizon expected discounted power utility of the consumption policies (controls). The default risk premium and the default intensity are assumed to rely on a stochastic factor formulated by a diffusion process. We study the optimal allocation and consumption policies to maximize the infinite horizon expected discounted non–log HARA utility of the consumption, and we use the dynamic programming principle to derive the Hamilton–Jacobi–Bellman (HJB) equation. Then we explore the HJB equation by employing a so–called sub–super solution approach. The optimal allocation and consumption policies are obtained in terms of the classical solution to a PDE. Finally, we get an explicit formula for the optimal control strategy. In this article The soloutions are then used in portfolio management subject to default risk and derive the optimal investment and consumption policies.<\div>
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