Showing papers by "Central Economics and Mathematics Institute published in 2013"

Bank cost efficiency in Kazakhstan and Russia

Abstract: In this paper, we estimate cost efficiency of the Kazakhstan and Russian banks. A stochastic frontier approach based on a panel data for 2002–6 is used. The Kazakhstan banking system is traditionally assumed to be more advanced compared to the Russian system. Empirically we do not find any significant differences in the cost efficiency of banks between these two countries during the period of our study. This result is found to be quite robust across several alternative and competing models. We also find that many of the banks in both countries operate below their optimal size.

On stochastic optimality for a linear controller with attenuating disturbances

Abstract: For a linear stochastic control system with quadratic objective functional, we introduce various generalizations of the notions of optimality on average and stochastic optimality on an infinite time interval that take into account possible degeneration of the parameter of the disturbing process with time (attenuation of the disturbances) or the presence of a discount function in the objective functional. This lets us improve upon the quality estimate for a well known optimal control in this problem from the point of view of both asymptotic behavior of the functional's expectation and its asymptotic probabilistic properties. In particular, in the considered case we have found an improvement for the well known logarithmic upper bound on the optimal control for a family of defect processes.

What Kind of Economy does Russia Need and for What Purpose? (An Attempt of System Analysis)

Abstract: Requirements for the economy as a subsystem of society are examined in the article, based on the analysis and development of the four-element model of society as the arena of interaction between state, socium, economy and business. Using the results of the new theory of socio-economic systems, we define the quality that the economy should have to meet the demands placed upon it by other macro-level subsystems. Among these qualities — diversification of the economy with respect to workplaces and business opportunities provided by implementing investment projects.

Essential Supremum with Respect to a Random Partial Order

Abstract: Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in $\R^d$ is lifted to the space $L^0(\R^d)$ of $d$-dimensional random variables. In contrast to the classical definition, we define the essential supremum as a subset of random variables satisfying some natural properties. An application of the introduced notion to a hedging problem under transaction costs is given.

Singular Problems for Integro-differential Equations in Dynamic Insurance Models

Abstract: A second-order linear integro-differential equation with Volterra integral operator and strong singularities at the endpoints (zero and infinity) is considered. Under limit conditions at the singular points, and some natural assumptions, the problem is a singular initial problem with limit normalizing conditions at infinity. An existence and uniqueness theorem is proved and asymptotic representations of the solution are given. A numerical algorithm for evaluating the solution is proposed; calculations and their interpretation are discussed. The main singular problem under study describes the survival (non-ruin) probability of an insurance company on infinite time interval (as a function of initial surplus) in the Cramer–Lundberg dynamic insurance model with an exponential claim size distribution and certain company’s strategy at the financial market assuming investment of a fixed part of the surplus (capital) into risky assets (shares) and the rest of it into a risk-free asset (bank deposit). Accompanying “degenerate” problems are also considered that have an independent meaning in risk theory.

Economic Miracle of Post-Soviet Space: Why Uzbekistan Managed to Achieve What No Other Post Soviet State Achieved

Abstract: Uzbekistan is not usually considered an economic success story, but in fact it is: its GDP increased since 1989 more than in any other post-communist country, except for China, Vietnam and Turkmenistan. The success of Uzbekistan is very much similar to the Chinese – gradual economic reforms with the preservation of the capacity of state institutions, good macroeconomic policy and export oriented industrial policy. What makes Uzbekistan unique is that no other former Soviet republic managed to follow this route. There are countries with healthy state finances and low inflation (most FSU states), there are some countries with reasonable state capacity (Baltics, Belarus, Azerbaijan, Turkmenistan, Kazakhstan), but there are no countries that keep undervalued exchange rate together with strong tax stimuli for export of manufactures. Uzbek example shows that such a policy pays off.

Level premium rates as a function of initial capital

Abstract: In Malinovskii (2012) , level premium rate and level initial capital were used to construct solvent and equitable strategies in a multi-period game model of risk. Focused there was the level initial capital regarded as a function of the annual premium rate. With the prospective goal to study adaptive control strategies on falling competitive insurance markets, in this paper we focus on the level premium rate regarded as a function of initial capital.

Mapping risk factors of innovation activity enterprises

Abstract: The paper proposes a five-stage procedure to analyse risk factors of innovation activity. The system of innovation activity factors is determined at the first stage. The second stage identifies the factors that have a negative impact on innovation activity. At the third stage, the data of the innovative innovation survey is completed by additional information to obtain indirect estimates of missing factors. To determine the relative scope and magnitude of the risk factors, their ranking takes place at the fourth stage. In addition, the mapping of risks and risk factors is the subject of the fifth stage. This stage leads to the construction of relevant problem spaces for innovation management and regulation. The map obtained provides opportunities for offering policy measures (at both state and enterprise levels) to mitigate, and compensate for, risks of innovation activity. The Russian enterprises’ statistics is used to construct an example of the map.

Essential Supremum and Essential Maximum with Respect to Random Preference Relations

Abstract: In the first part of the paper we study concepts of supremum and maximum as subsets of a topological space X endowed by preference relations. Several rather general existence theorems are obtained for the case where the preferences are defined by countable semicontinuous multi-utility representations. In the second part of the paper we consider partial orders and preference relations "lifted" from a metric separable space X endowed by a random preference relation to the space L^0(X)X-valued random variables. We provide an example of application of the notion of essential maximum to the problem of the minimal portfolio super-replicating an American-type contingent claim under transaction costs.

On Supremal and Maximal Sets with Respect to Random Partial Orders

Abstract: The paper deals with definition of supremal sets in a rather general framework where deterministic and random preference relations (preorders) and partial orders are defined by continuous multi-utility representations. It gives a short survey of the approach developed in [4], [5] with some new results on maximal sets.

A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure

Abstract: Lomonosov Moscow State UniversityFaculty of Computational Mathematics and CyberneticsRussia, Moscow, Leninskiye Gory, MSUe-mail: barbudo.sam@cs.msu.suAbstractWe consider a problem of maximization of the distance traveled by amaterial point in the presence of a nonlinear friction under a bounded thrustand fuel expenditure. Using the maximum principle we obtain the form ofoptimal control and establish conditions under which it contains a singularsubarc. This problem seems to be the simplest one having a mechanicalsense in which singular subarcs appear in a nontrivial way.Keywords: optimal control problem, Pontryagin Maximum Principle,extremals, singular arcs.2010 Mathematics Subject Classification: 49K15, 49N90.

Rationale of underwriters’ pricing conduct on competitive insurance market

Abstract: Underwriters’ desire to show a good annual review is known to be a rationale of the aggressive pricing conduct. On the competitive insurance market, it impacts the global insurance processes and can lead to the competition-originated underwriting cycles. Applying Lundberg’s model of the annual probability mechanism of insurance, we model the influence of a price reduction on migration and consequently on the company’s annual expansion, revenue and solvency.

Optimal synthesis in the Reeds and Shepp problem with a free final direction

Abstract: We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a free final direction of velocity. Using Pontryagin maximum principle, we obtain all types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis.

Whither Income Inequalities

Abstract: Some major trends in world income inequalities and relevant economic trends are reviewed here. In recent decades, there have been indications of a reversal of the growing income divergence between North and South after over half a millennium, especially in the last two centuries. Meanwhile, income inequalities within most countries have been growing again, increasing social tensions, which may jeopardize growth in some countries and reshape global economic competition. In the 1960s, when the profit rate and capital’s share of national income in Western countries were highest, income inequality within countries was at a historical low. Since the 1980s, the increasing share of profits in national income and rising inequality within countries have gone hand in hand.

A Mathematical Model of Investment Incentives

Abstract: An investment timing problem which takes into account both taxation (including tax exemptions) and financing by credit is considered. This problem is reduced to the optimal stopping of a two-dimensional diffusion process. We give the solution to the investment timing problem as a function of parameters of the model, in particular, of the tax holiday duration and interest rate for borrowing. We study the question whether the higher interest rate for borrowing can be compensated by tax holidays.

Bishop-Runge approximations and inversion of a Riemann-Klein theorem

Abstract: In this paper we give results about projective embeddings of Riemann surfaces, smooth or nodal, which we apply to the inverse Dirichlet-to-Neumann problem and to the inversion of a Riemann-Klein theorem. To produce useful embeddings, we adapt a technique of Bishop in the open bordered case and use Runge type harmonic approximation theorem in the compact case.

Optimal Synthesis in the Reeds and Shepp Problem with Onesided Variation of Velocity

Abstract: We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of the velocity. Using the Pontryagin Maximum Principle, we obtain all possible types of extremal and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis.

Tendencies and Key Factors in the Health of School Students.

Abstract: According to research data, in today's Russia 70 percent of children are born with various health risk factors, and this leads to a rapid deterioration of their health during their school years. The health of school students is getting worse as a consequence of the effect of a whole set of social and economic and psychological factors, and the only way to change these negative trends is through the joint efforts of parents, the system of health care, education, and state programs.