Construction of Nonlinear Stabilizer for Trajectories of Economic Growth

A dynamic model of optimization of R&D intensity is studied for analyzing the effect of the spillover technology assimilation on techno-economic growth. The research focuses on the issue of a reasonable balance in the R&D investment policy between the indigenous technology stock and exogenous technology flow. On the basis of the concavity properties of the Hamiltonian, a nonlinear stabilizer sustaining proportional techno-economic growth is constructed. Trends of optimal R&D intensity are examined depending on the values of the model macroeconomic parameters and the feedback variables. Econometric analysis shows that additional investments and restructuring of these sources for knowledge absorption could have the effect of increasing returns and provide a strong leverage for reaching qualitatively higher levels of sales, technology development, and consumption index. The research was sponsored by the SIMOT Program of the Japanese Ministry of Education, Science and Technology. A.M. Tarasyev was supported by the Russian Fund for Basic Research, Grants 05-01-00601, 05-01-08034, Russian Fund for Humanities, Grant RFH 05-02-02118a, and by the Program for the Sponsorship of Leading Scientific Schools, Grant NSCH-791.2003.1.     

A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper. For claim sizes with common distribution of extended regular variation, we study the asymptotic behaviour of the ruin probability. As a corollary, we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims. This work was supported by National Natural Science Foundation of China (Grant Nos. 10571167, 70501028), the Beijing Sustentation Fund for Elitist (Grant No. 20071D1600800421), the National Social Science Foundation of China (Grant No. 05&ZD008) and the Research Grant of Renmin University of China (Grant No. 08XNA001)     

The option value of advanced R & D

Existing tools for making R&D investment decisions cannot properly capture the option value in R&D. Since many new products are identified as failures during the R&D stages, the possibility of refraining from market introduction may add a significant value to the NPV of the R&D project. This paper presents new theoretical insight by developing a stochastic jump amplitude model in a real setting. The option value of the proposed model depends on the expected number of jumps and the expected size of the jumps in a particular business. The model is verified with empirical knowledge of current research in the field of multimedia at Philips Corporate Research. This way, the gap between real option theory and the practice of decision making with respect to investments in R&D is diminished.     

Modelling of technology lifetime based on patent citation data and segmentation

Stakeholders faced with decisions on whether or not to invest in Research & Development (R&D) are increasingly in need of R&D supporting information. As such, the social demand for reliable methods to collect and assess such data continues to grow. In terms of technology appraisal and valuation, the economic life span is a particularly important factor that affects the size of the profit resulting from that technology. Here, we propose a new methodology for quantitatively estimating the technology lifetime based on patent citation data and segmentation. Using the proposed methodology, we are able to estimate the mean or median patent lifetime at both the technology group level and the individual patent level. The estimated technology lifetime may be used as an index for supporting decision-making on strategic investments related to R&D activities and for managing technology throughout its lifecycle, including R&D planning, development, and application. We have applied the proposed methodology to US patent data for the period 1976–2004 for four communications areas.     

Optimal Dynamics of Innovation in Models of Economic Growth

A nonlinear model of economic growth which involves production, technology stock, and their rates as the main variables is considered. Two trends (growth and decline) in the interaction between the production and R&D investment are examined in the balanced dynamics. The optimal control problem of R&D investment is studied for the balanced dynamics and the utility function with the discounted consumption. The Pontryagin optimality principle is applied for designing the optimal nonlinear dynamics. An existence and uniqueness result is proved for an equilibrium of the saddle type and the convergence property of the optimal trajectories is shown. Quasioptimal feedbacks of the rational type for balancing the dynamical system are proposed. The growth properties of the production rate, R&D, and technology intensities are examined on the generated trajectories.     

Productivity and technical changes in the Indian pharmaceutical industry

We study the productivity change and factors driving this change in the Indian pharmaceutical industry during 1994–2003, in the backdrop of economic liberalization and change in regulatory norms. We use a non parametric Data Envelopment based-methodology to estimate productivity change and decompose it into technical and relative efficiency changes. We find that, the long-term strategic measures by a section of innovative firms that foresaw the implications from competitive forces of globalization and a change in the regulatory environment have sphereheaded the technical change. Consequently, few innovative firms, characterized by greater R&D investments, transition into higher value-added products and businesses as a step towards more technically sophisticated new drug development have pushed the production frontier, increasing the technical and productivity gains. The higher technical and R&D capabilities and wider new product portfolios of multinational companies also have contributed to the positive technical and productivity changes in the Indian pharmaceutical industry.     

Finite groups in which elements of the same order outside the center are conjugate

We prove that if G is a finite group in which the elements of the same order outside the center are conjugate,then either G is abelian or G(?)S_3.     

Justification of Dipole Approximation in the Problem of Nonlinear Wave Generation by a Submerged Sphere

Some nonlinear dipole approximation is constructed for the nonstationary problem of a solid sphere motion under a free surface. The approximation is justified in the class of analytic functions decaying at infinity.Original Russian Text Copyright © 2005 Pyatkina E. V.The author was supported by the State Maintenance Program for the Leading Scientific Schools (Grant NSh-440.2003.1) and the Russian Foundation for Basic Research (Grant 05-01-00250).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 907–927, July–August, 2005.     

On Recognition by Spectrum of Finite Simple Linear Groups over Fields of Characteristic 2

A finite group G is said to be recognizable by spectrum, i.e., by the set of element orders, if every finite group H having the same spectrum as G is isomorphic to G. We prove that the simple linear groups L _n (2^k) are recognizable by spectrum for n = 2^m ≥ 32.Original Russian Text Copyright © 2005 Vasil’ev A. V. and Grechkoseeva M. A.The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-00797), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2069.2003.1), the Program “ Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 8294), the Program “Universities of Russia” (Grant UR.04.01.202), and a grant of the Presidium of the Siberian Branch of the Russian Academy of Sciences (No. 86-197).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 749–758, July–August, 2005.     

On functional equations satisfied by spinor Euler products for Siegel modular forms of genus 2 with characters

It is proved under certain assumptions that spinor Euler products for Siegel eigen cusp forms with characters with respect to the groups Γ² ₀(q) have holomorphic analytical continuation over the whole complex plane and satisfy a functional equation with two gamma-factors. The author was supported in part by Russian Fund of Fundamental Researches, Grant # 99-01-00099.     

Dynamic Model of R&D,Spillovers, and Efficiency of Bertrand and Cournot Equilibria

Using an infinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes, and spillovers are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.     

Solving elliptical equations with high-contrast coefficients in an unbounded region

An approximation model is proposed for an elliptical equation with complex rapidly varying coefficients. An efficient numerical method is developed and implemented. A problem of geoelectricity requiring solution of an equation in this setting is investigated. This research was partially supported by the Russian Foundation for Basic Research (grant No. 96-05-64340) and by the Interuniversity Scientific Program “Russian Universities: Basic Research.” Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 37–45, 1998.     

Optimal choice of threshold in Two Level Processor Sharing

We analyze the Two Level Processor Sharing (TLPS) scheduling discipline with the hyper-exponential job size distribution and with the Poisson arrival process. TLPS is a convenient model to study the benefit of the file size based differentiation in TCP/IP networks. In the case of the hyper-exponential job size distribution with two phases, we find a closed form analytic expression for the expected sojourn time and an approximation for the optimal value of the threshold that minimizes the expected sojourn time. In the case of the hyper-exponential job size distribution with more than two phases, we derive a tight upper bound for the expected sojourn time conditioned on the job size. We show that when the variance of the job size distribution increases, the gain in system performance increases and the sensitivity to the choice of the threshold near its optimal value decreases. The work was supported by France Telecom R&D Grant “Modélisation et Gestion du Trafic Réseaux Internet” no. 46129414.     

Can R&D expenditure avoid corporate bankruptcy? Comparison between Japanese machinery and electric equipment industries using DEA–discriminant analysis

This study compares data envelopment analysis–discriminant analysis (DEA–DA) with Altman’s financial ratio analysis to identify the position of DEA–DA in financial performance analysis. Then, this study applies DEA–DA to examine whether Research and Development (R&D) expenditure influences the financial performance of Japanese machinery industry and electric equipment industry. The investigation of DEA–DA identifies that the R&D expenditure makes a positive impact on the financial performance of Japanese machinery industry, but it yields a negative impact on Japanese electric equipment industry. The result implies that the influence of R&D expenditure on financial performance (including the avoidance of bankruptcy) depends upon the type of a manufacturing industry. A rationale regarding why such a discrepancy has occurred between the two Japanese manufacturing industries is because the life cycle of electric equipments is shorter than that of the machinery products. Furthermore, the electric equipment industry faces more fierce competition than the machinery industry. This study suggests that the Japanese electric equipment industry needs R&D expenditure for competition in its global market. However, it is a high risk and high return investment. In contrast, the Japanese machinery is a technologically mature industry where the R&D expenditure influences positively its financial performance. In this sense, the R&D expenditure is a low risk and necessary investment.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

Numerical analysis of geoelectric fields in a medium with faults

An efficient method of electromagnetic field calculation is applied to the model of a multilayer nonhomogeneous medium with an arbitrary number of vertical faults. The model simulates a medium that includes the asthenosphere, the crustal layer, and the surface sedimentary layer, all joined by conducting faults. The numerical results are calculated and the effect of faults is assessed. This research was partially supported by the Russian Foundation for Basic Research (grant No. 96-05-64340) and by the Interuniversity Scientific Program “Russian Universities: Basic Research.” Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 85–93, 1998.     

On Differential Equations with Retarded Argument

We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program Development of the Scientific Potential of Higher School of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005.     

Strategic Planning and the Investment-Financing Behaviour of Major Industrial Companies

The hypothesis that firms simultaneously determine their research and development, investment, dividend and effective-debt policies generally is substantiated in the financial literature. The determinants of research and development, dividend, investment and financing decisions of 303 firms are estimated econometrically during the 1976-1982 period. Moreover, an optimization model is estimated for a firm that seeks to minimize underachievement of desired investments, dividend and R&D and minimize the underachievement of desired effective debt. Management gains additional insights to increase the achievement of maximizing research and development expenditures at the expense of paying dividends and undertaking investments.