Central Economics and Mathematics Institute

About: Central Economics and Mathematics Institute is a facility organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Foreign-exchange reserves. The organization has 297 authors who have published 580 publications receiving 6449 citations. The organization is also known as: Federal State Institution of Science Central Economics and Mathematics Institute of the Russian Academy of Sciences.

Analytic-Numerical Investigations of Singular Problems for Survival Probability in the Dual Risk Model with Simple Investment Strategies

Abstract: We study the life annuity insurance model when simple investment strategies (SISs) of the two types are used: risky investments and risk-free ones. According to a SIS of the first type, the insurance company invests a constant positive part of its surplus into a risky asset while the remaining part is invested in a risk-free asset. A risk-free SIS means that the whole surplus is invested in a risk-free asset. We formulate and study some associated singular problems for linear integro-differential equations (IDEs). For the case of exponential distribution of revenue sizes, we state that survival probabilities as the functions of the initial surplus (IS) are unique solutions of the corresponding problems. Using the results of computational experiments, we conclude that in the region of small sizes of IS the risky SIS may be more effective tool for increasing of the survival probability than risk-free one.

Bilevel Optimal Tolls Problems with Nonlinear Costs: A Heuristic Solution Method

Abstract: We consider a bilevel programming problem modeling the optimal toll assignment as applied to an abstract network of toll and free highways. A public governor or a private lease company run the toll roads and make decisions at the upper level when assigning the tolls with the aim of maximizing their profits. The lower level decision makers (highway users), however, search an equilibrium among them while trying to distribute their transportation flows along the routes that would minimize their total travel costs subject to the satisfied demand for their goods/passengers. Our model extends the previous ones by adding quadratic terms to the lower level costs thus reflecting the mutual traffic congestion on the roads. Moreover, as a new feature, the lower level quadratic costs aren’t separable anymore, i.e., they are functions of the total flow along the arc (highway). In order to solve the bi-level programming problem, a heuristic algorithm making use of the sensitivity analysis techniques for quadratic programs is developed. As a remedy against being stuck at a local maximum of the upper level objective function, we adapt the well-known “filled function” method which brings us to a vicinity of another local maximum point. A series of numerical experiments conducted on test models of small and medium size shows that the new algorithm is competitive enough.