A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the f... more A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the first or the last payment may be incomplete, when the amount of the other payments are predetermined. In the nonlinear optimization model, which we propose in this paper, we assume that the creditor wants to construct the amortization schedule for repayment of a loan with minimal risk of default. For this purpose he must determine the optimal pair of the duration of the loan and the amount of the payments. On the base of the model considered, we propose a necessary and sufficient condition for optimality of this pair.
We consider a class of age-structured control problems with nonlocal dynamics and boundary condit... more We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).
We consider a class of age-structured control problems with state constraints, nonlocal dynamics ... more We consider a class of age-structured control problems with state constraints, nonlocal dynamics and boundary conditions, defined on finite time intervals. For these problems we suggest Mangasarian-type suf-ficient conditions for the optimality of the control. As an application we consider a model with a state constraint of optimal investment in vintage capital goods. To solve this model we suggest a numerical method and we prove that this method converges to an optimal solution.
A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the f... more A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the first or the last payment may be incomplete, when the amount of the other payments are predetermined. In the nonlinear optimization model, which we propose in this paper, we assume that the creditor wants to construct the amortization schedule for repayment of a loan with minimal risk of default. For this purpose he must determine the optimal pair of the duration of the loan and the amount of the payments. On the base of the model considered, we propose a necessary and sufficient condition for optimality of this pair.
A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the f... more A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the first or the last payment may be incomplete, when the amount of the other payments are predetermined. In the nonlinear optimization model, which we propose in this paper, we assume that the creditor wants to construct the amortization schedule for repayment of a loan with minimal risk of default. For this purpose he must determine the optimal pair of the duration of the loan and the amount of the payments. On the base of the model considered, we propose a necessary and sufficient condition for optimality of this pair.
We consider a class of age-structured control problems with nonlocal dynamics and boundary condit... more We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).
We consider a class of age-structured control problems with state constraints, nonlocal dynamics ... more We consider a class of age-structured control problems with state constraints, nonlocal dynamics and boundary conditions, defined on finite time intervals. For these problems we suggest Mangasarian-type suf-ficient conditions for the optimality of the control. As an application we consider a model with a state constraint of optimal investment in vintage capital goods. To solve this model we suggest a numerical method and we prove that this method converges to an optimal solution.
A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the f... more A loan is typically repaid by equal payments at equal time intervals. Besides the amount of the first or the last payment may be incomplete, when the amount of the other payments are predetermined. In the nonlinear optimization model, which we propose in this paper, we assume that the creditor wants to construct the amortization schedule for repayment of a loan with minimal risk of default. For this purpose he must determine the optimal pair of the duration of the loan and the amount of the payments. On the base of the model considered, we propose a necessary and sufficient condition for optimality of this pair.
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Papers by Vladimir Krastev