Markets for emission permits with free endowment: a vintage capital analysis

In this paper we develop a vintage capital model for a firm involved in a market for tradable emission permits. We analyze both the firm’s optimal investment plans and the market equilibrium. This allows us to scrutinize how firms use permits free endowment, and to highlight the implications of non-optimal uses both at the firm and at the market level. We provide a new rationale for the market of tradable permits not to be cost-efficient. The novel technical points in this context are the use a distributed (vintage) optimal control model of the firm, the use of optimality conditions for non-smooth problems, and the involvement of a nonlinear Fredholm integral equation of the first kind for the description of the equilibrium price of permits, and its practical meaning for market regularization.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.Let M be a complete C1−Finsler manifold without boundary and f : M → R be a locally Lipschitz function. The classical proof of the well known deformation lemma can not be extended in this case because integral lines may not exist. In this paper we establish existence of deformations generalizing the classical result. This allows us to prove some known results in a more general setting (minimax theorem, a theorem of Ljusternik-Schnirelmann type, mountain pass theorem). This approach enables us to drop the compactness assumptions characteristic for recent papers in the field using the Ekeland’s variational principle as the main tool

L-Spline Interpolation for Differential Operators of Order 4 with Constant Coefficients

In this paper it is shown that many features from polynomial spline methods used in nonparametric regression and smoothing procedures carry over to the class of L-splines where L is a linear differential operator of order 4 with constant coefficients. Special attention is given to the question whether an analogue of the Reinsch algorithm is valid and criteria are given such that the associated matrix R is strictly diagonal dominant.Project KP-06-N32-8; Project KP-06N42-2 with Bulgarian NSF; Grant No BG05M2OP001-1.001-0003,financed by the Science and Education for Smart Growth Operational Program (2014-2020) and co-financed by the European Union through the European structural and Investment funds

Оптимално управление на хетерогенни системи

Цветомир Цачев - В настоящия доклад се прави преглед на някои резултати от областта на оптималното управление на непрекъснатите хетерогенни системи, публикувани в периодичната научна литература в последните години. Една динамична система се нарича хетерогенна, ако всеки от нейните елементи има собствена динамиката. Тук разглеждаме оптимално управление на системи, чиято хетерогенност се описва с едномерен или двумерен параметър – на всяка стойност на параметъра отговаря съответен елемент на системата. Хетерогенните динамични системи се използват за моделиране на процеси в икономиката, епидемиологията, биологията, опазване на обществената сигурност (ограничаване на използването на наркотици) и др. Тук разглеждаме модел на оптимално инвестиране в образование на макроикономическо ниво [11], на ограничаване на последствията от разпространението на СПИН [9], на пазар на права за въглеродни емисии [3, 4] и на оптимален макроикономически растеж при повишаване на нивото на върховите технологии [1]. Ключови думи: оптимално управление, непрекъснати хетерогенни динамични системи, приложения в икономиката и епидемиолегиятаThe present paper is a survey on some results on optimal control of continuous heterogeneous systems, which were recently published in periodic journals. A dynamical system is called heterogeneous if each of its elements has specific dynamics. The heterogeneity of the systems we consider is described by a one- or two-dimensional parameter – each element of the system corresponds to a specific value of the parameter. The heterogeneous dynamical systems are used to model processes in economics, epidemiology, biology, social security (preventing the use of illicit drugs) etc. Here we consider models of optimal investment in education at the macroeconomic level [11], of restricting the damage caused by the spread of HIV [9], of markets for emission permits [3, 4] and optimal macroeconomic growth with endogenous improvement of the cutting-edge technologies [1]. *2010 Mathematics Subject Classification: 49K20, 92C60, 35Q91, 37N40, 91B69

Markets for emission permits with free endowment: a vintage capital analysis

In this paper, we develop a vintage capital model for a firm involved in a market for tradable emission permits. We analyze both the firm's optimal investment plans and the market equilibrium. This allows us to scrutinize how firms use permits free endowment, and to highlight the implications of non-optimal uses both at the firm and at the market level. We provide a new rationale for the market of tradable permits not to be cost-efficient. The novel technical points in this context are the use of a distributed (vintage) optimal control model of the firm, the use of optimality conditions for non-smooth problems, and the involvement of a nonlinear Fredholm integral equation of the first kind for the description of the equilibrium price of permits, and its practical meaning for market regularization

The intrinsic mountain pass principle

NO ABSTRAC

MAXIMUM PRINCIPLE FOR AGE AND DURATION STRUCTURED SYSTEMS: A TOOL FOR OPTIMAL PREVENTION AND TREATMENT OF HIV

Age and duration since infection are considered in a model of optimal control of the spread of Human Immunodeficiency Virus (HIV) in countries with high prevalence. Prevention and medical treatment are selected so as to maximize an economic objective function.The model extends the classical McKendrick equation. Necessary optimality conditions in the form of Pontryagin's global maximum principle and numerical solution based on them are presented. “Critical” initial prevalence is established numerically for which there are two optimal medical treatments: one intense and another less demanding. It is shown that treatment alone can be counterproductive: increase in treatment must be accompanied by increase in prevention.age-structured systems, population dynamics, McKendrick equation, Pontryagin's maximum principle, infectious diseases, HIV,

Asen L. Dontchev (on the occasion of his 65th birthday) and Vladimir M. Veliov (on the occasion of his 60th birthday)

[Donchev Tzanko; Дончев Цанко]; [Krastanov Mikhail; Кръстанов Михаил]; [Ribarska Nadezhda; Рибарска Надежда]; [Tsachev Tsvetomir; Цачев Цветомир]; [Zlateva Nadia; Златева Надя