CURRICULUM VITAE
Name: Vladimir
Second name: Evgenevich
Surname: Bening
Date and place of birth: 29 June 1954, Konstantinovka
Home address: 7–3–6, Rusakovskaya str., Moscow, 107140, Russia
Home telephone: 7 (499) 264 79 47
Scientific degree: Doctor of Sciences in Physics and Mathematics, 1998
Academic title: Full Professor, 2005
Affiliation: Department of Mathematical Statistics, Faculty of Computational Mathem
atics and Cybernetics, Moscow State University
Present position: Professor, 2000
Office address: Faculty of Computational Mathematics and Cybernetics, Moscow State
University, Vorobyovy Gory, Moscow, 119899, Russia
Office telephone: 7 (495) 939 53 94
Fax: 7 (495) 939 25 96
E-mail: bening@yandex.ru
Passportl: 66N8432911, date of issue: 21.11.2023, date of expiry: 21.11.2028, authority:
MFA of Russia
Scientific interests: Asymptotic methods in mathematical statistics, limit theorems of
probability theory and their applications to physics, risk theory, insurance and finance, quality control and diagnostics
Publications: More than 240 including six monograph and six textbook
Courses read: Mathematical statistics; Risk theory; Insurance mathematics; Mathematical methods of discrimination analysis and pattern recognition; Probability theory and mathematical statistics; Applied statistics.
Main theoretical problems of interest
and obtained results
Asymptotic expansions and the deficiency concept in statistics: Asymptotic expansions and the formula for deficiency in the problems of hypotheses testing were constructed for the most widely used test statistics such as L-statistics, R-statistics and U-statistics. Similar results were obtained for power functions and deficiencies.
Convergence rate estimates were constructed as well.
R E F E R E N C E S:
1. V. E. Bening. Asymptotic Theory of Testing Statistical Hypotheses: Efficient Statistics, Optimality, Deficiency. VSP, Utrecht, 2000.
2. V. E. Bening. A formula for deficiency: one-sample L− and R− tests. I, II. — Mathematical Methods of Statistics, 1995, vol. 4, p. 167-188, 274-293.
3. V. E. Bening. Convergence rate estimates under alternatives. — Soviet Math. Dokl., 1996, vol. 349, p. 151-152.
4. V. E. Bening. On the deficiency of a two-sample rank test. — Theory Probab. Appl., 1999, vol. 44, No. 1, p. 159-161.
5. V. E. Bening. On the asymptotic deficiency of some bayesian criteria. — Journal of Math. Sciences, 2013, vol. 189, No. 6, p. 967-975.
Compound Cox processes: Compound Cox processes (doubly stochastic Poisson processes) are very flexible and adequate mathematical models of inhomogeneous chaotic
flows of events. Based on the general theorem on limit behavior of superpositions of independent random processes, a rather complete description was obtained of the asymptotic behavior of compound Cox processes with both zero and non-zero means as well as of their extremes. These results include convergence criteria, the description of limit laws, convergence rate estimates. In joint papers with V. Yu. Korolev,the asymptotic expansions were constructed for the distributions of compound Cox processes as well as for their quantiles. Estimates for the concentration functions of these processes were also obtained.
R E F E R E N C E S:
1. V. E. Bening, V.Yu. Korolev. Generalized Poisson Models and their Applications in Insurance and Finance. VSP, Utrecht, 2002.
2. V. E. Bening and V. Yu. Korolev. On approximations to generalized Cox processes, Probability and Mathematical Statistics (Wroc law), 1998, Vol. 18, No. 2, p. 247-270.
3. V. E. Bening and V. Yu. Korolev. Asymptotic behavior of non-ordinary generalized Cox processes with nonzero means. — Journal of Mathematical Sciences, 1998, Vol. 92, No. 3, p.3836-3856.
4. V. E. Bening. On estimation of Student distribution center with a small number of degrees of fridom. — Journal of Math. Sciences, 2013, vol. 189, No. 6, p. 889-898.
Main applied problems of interest
and obtained results
Reliability theory: The accuracy of estimators of failure-free performance characteristics was investigated for small samples. These results were applied to analysing reliability of aerospace equipment.
R E F E R E N C E S:
1. V. E. Bening and A. A. Tin’kov. On the accuracy of estimators of failure-free performance characteristics of aviation technics from on small samples. — Bulletin of N. E. Zhukovskii Military Engineering Academy, 1996, p. 125-142.
2. V. E. Bening and A. I. Buravlev. A recurrence procedure of non-parametric estimation of distributions from small samples. — Bulletin of N. E. Zhukovskii Military Engineering Academy, 1988, p. 97-130.
3. V. E. Bening. Statistical estimation of parameters of fractionally stable distributions. — Journal of Math. Sciences, 2013, vol. 189, No. 6, p. 899-902.
Numerical methods of solving integro-differential equations:
An effective numerical method was proposed for solving Navier–Stokes differential equations describing aerodymamical processes in aerospace equipment.
R E F E R E N C E S:
1. V. E. Bening. On a method of solving partially smoothed Navier–Stokes equations. — Bulletin of N. E. Zhukovskii Military Engineering Academy, 1986, p. 52-54.
2. V. E. Bening and A. I. Zhelannikov. Locally individual smoothing in turbulence problems. — Bulletin of N. E. Zhukovskii Military Engineering Academy, 1986, p. 55-61.
Insurance: New mathematical models were constructed for the description of function
ing of insurance companies. Generalized risk processes were studied. These processes are natural generalizations of the classical risk process with constant premium rate and Poisson flow of claims. In order to construct a more flexible mathematical model for the surplus of an insurance company it is reasonable to take into account both risk and portfolio fluctuations. It can be shown that under risk fluctuations (non constant intensity of insurance payments), in reasonable strategies of the insurer the premium rate or, which is in some sense the same, the current size of the portfolio must not be constant. On the other hand, the intensity of payments should be proportional to the current number of insurance contracts in the portfolio resulting in that the cumulative stochastic intensity of payments should be proportional to the total number of contracts in the portfolio or, which is in some sense the same, to the cumulative premiums. This reasoning quite naturally leads to the generalized risk processes which are obtained from classical risk processes by means of stochastic change of time. The asymptotic behavior of these processes was investigated in full detail. The obtained results provide serious theoretical grounds for the construction of reasonable (asymptotic) approximations for the distribution of the total claim size as well as for that of the surplus of an insurance company. Both point and interval nonparametric statistical estimators were constructed for the ruin probability in generalized risk processes. Non-classical optimization problems were considered for non-homogeneous risk processes.
R E F E R E N C E S:
1. V. E. Bening, V.Yu. Korolev. Generalized Poisson Models and their Applications in Insurance and Finance. VSP, Utrecht, 2002.
2. V. E. Bening and V. I. Rotar’. A model of optimal behavior of insurance company. — Economics and Math. Methods, 1993, vol. 29, p. 617-626.
3. V. E. Bening and V. I. Rotar’. An introduction to the mathematical theory of insurance. — Surveys in Industrial and Applied Mathematics, ser. Financial and Insurance Mathematics, 1994, vol. 1, p. 698-779.
4. V. E. Bening and V. Yu. Korolev. Statistical estimation of ruin probability for generalized risk processes. — Theory of Probability and its Applications, 1999, Vol. 44, No. 1, p. 161-164.
5. V. E. Bening. On rate of convergence in distribution of asymptotically normal statistics based on samples of random size. — Annales Mathematicae et Informaticae, 2012, vol. 39, p. 17-28.
