Optimal investment and reinsurance of an insurer with model uncertainty

We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.     

The solution of linear and nonlinear systems of Volterra functional equations using Adomian–Pade technique

The purpose of this study is to implement Adomian–Pade (Modified Adomian–Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian–Pade (Modified Adomian–Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM–PADE (MADM–PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM).     

On the existence of certain cyclic difference families and difference matrices

A theorem is proved to the effect that if there exists a BIB-schema with parameters (p^m–1,k, k–1), where k¦(p^m–1), p is prime, and m is a natural number, then there exists a BIB-schema (p^mn–1),k, k–1). A consequence is the existnece of a cyclic BIB-schema (p^mn–1, p^m–1, p^m–2) (p^m–1 is prime) that specifies each ordered pair of difference elements at any distance = 1, 2, ..., p^m–2 (cyclically) precisely once. Recursive theorems on the existence of difference matrices and (v, k, k)-difference families in the group Z_v of residue classes mod v are proved, along with a theorem on difference families in an additive abelian group.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 114–119, July, 1992.     

Generalized z-Distributions and Related Stochastic Processes

The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.     

The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices

In this paper, we first determine the maximal and minimal ranks of A — BXC with respect to X. Using those results, we then find the maximal and minimal ranks of the expressions AA^– — A^– A — BB^– A — AC^– C and B^– BA — ACC^– with respect to the choice of generalized inverses A^–, B^– and C^–. In particular, we consider the commutativity of A and A^–, A^k and A^–.The research of the author was supported in part by the Natural Sciences and Engineering Research Council of Canada.     

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems

Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali–Hahn–Saks theorem are given.     

Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

We show that three important topics in nonlinear analysis and optimization are intimately related: the theory of perturbations, the notion of well-posedness and variational principles in the sense of Ekeland, Borwein–Preiss and Deville–Godefroy–Zizler. The concept of genericity and the new notion of flexible perturbation play a key role in these connections. This notion enables one to consider topologies on spaces of functions which have been introduced recently. A link between the Asplund and Ekeland–Lebourg methods and the Palais–Smale condition, another important topic in nonlinear analysis, is pointed out.     

Symmetric Gauss–Lobatto and Modified Anti-Gauss Rules

The present paper is concerned with symmetric Gauss–Lobatto quadrature rules, i.e., with Gauss–Lobatto rules associated with a nonnegative symmetric measure on the real axis. We propose a modification of the anti-Gauss quadrature rules recently introduced by Laurie, and show that the symmetric Gauss–Lobatto rules are modified anti-Gauss rules. It follows that for many integrands, symmetric Gauss quadrature rules and symmetric Gauss–Lobatto rules give quadrature errors of opposite sign.     

Finitistic dimension and Igusa–Todorov algebras

The notion of Igusa–Todorov algebras is introduced in connection with the (little) finitistic dimension conjecture, and the conjecture is proved for those algebras. Such algebras contain many known classes of algebras over which the finitistic dimension conjecture holds, e.g., algebras with the representation dimension at most 3, algebras with radical cube zero, monomial algebras and left serial algebras, etc. It is an open question whether all artin algebras are Igusa–Todorov. We provide some methods to construct many new classes of (2-)Igusa–Todorov algebras and thus obtain many algebras such that the finitistic dimension conjecture holds. In particular, we show that the class of 2-Igusa–Todorov algebras is closed under taking endomorphism algebras of projective modules. Hence, if all quasi-hereditary algebras are 2-Igusa–Todorov, then all artin algebras are 2-Igusa–Todorov by [V. Dlab, C.M. Ringel, Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring, Proc. Amer. Math. Soc. 107 (1) (1989) 1–5] and have finite finitistic dimension.     

Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions

We prove that the kernels of the Baskakov–Durrmeyer and the Szász–Mirakjan–Durrmeyer operators are completely monotonic functions. We establish a Bernstein type inequality for these operators and apply the results to the quasi-interpolants recently introduced by Abel. For the Baskakov–Durrmeyer quasi-interpolants, we give a representation as linear combinations of the original Baskakov–Durrmeyer operators and prove an estimate of Jackson–Favard type and a direct theorem in terms of an appropriate K-functional.     

State of stress and strain of plates with two equal openings in the presence of high-elastic deformation

The apparatus of the nonlinear theory of elasticity [1–3] is used to investigate the high-elastic deformation of a plate with two equal circular openings and a massive block with two cylindrical channels. Computer-calculated stress concentration factors are given for compressible and incompressible materials.Translated from Mekhanika Polimerov, No. 4, pp. 687–692, July–August, 1969.     

Precise distribution properties of the van der Corput sequence and related sequences

The discrepancy is a quantitative measure for the irregularity of distribution of sequences in the unit interval. This article is devoted to the precise study of L_p–discrepancies of a special class of digital (0,1)–sequences containing especially the van der Corput sequence. We show that within this special class of digital (0,1)–sequences over ℤ₂ the van der Corput sequence is the worst distributed sequence with respect to L₂–discrepancy. Further we prove that the L_p–discrepancies of the van der Corput sequence satisfy a central limit theorem and we study the discrepancy function of (0,1)–sequences pointwise.     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

A Family of Semi-Regular Divisible Difference Sets

We give a construction of semi-regular divisible difference sets with parametersm = p2a(r–1)+2b (pr – 1)/(p – 1), n = pr, k = p(2a+1)(r–1)+2b (pr – 1)/(p – 1)1 = p(2a+1)(r–1)+2b (pr–1 – 1)/(p-1), 2 = p2(a+1)(r–1)–r+2b (pr – 1)/(p – 1)where p is a prime and r a + 1.     

A Clifford–Finslerian physical unification and fractal dynamics

A Clifford–Finslerian physical unification is proposed based on Clifford–Finslerian mathematical structures and three physical principles. In the Clifford–Finslerian mathematical structure, spontaneous symmetry breaking is automatically embedded in fractal branches. With the action principle, connection principle and computation principle, physics can be unified, in which the Riemman–Einstein system and Euclid–Newton system are naturally included when quaternion are reduced to complex and real phases.     

Integrable Chains and Hierarchies of Differential Evolution Equations

A class of integrable differential–difference systems is constructed based on auxiliary linear equations defined on sequences of Zakharov–Shabat formal dressing operators. We show that the auxiliary equations are compatible with the evolution equations for the Kadomtsev–Petviashvili (KP) hierarchy. The investigation results are used to elaborate a modified version of Krichever rational reductions for KP hierarchies.     

Ultratertiary Quantization of Thermodynamics

We show that if the Dirac–Bogoliubov rule for replacing the bosonic creation and annihilation operators with the c-numbers is used, then the ultratertiary quantization allows obtaining the Bardeen–Cooper–Schrieffer–Bogoliubov formulas.     

Melting of Two-Dimensional Systems: Dependence of the Type of Transition on the Radius of the Potential

In the framework of the two-dimensional melting theory based on the density functional approach, we use a Monte Carlo computer simulation to study melting of a two-dimensional hard disk system with a rectangular-well attraction potential. We show that depending on the attraction radius, the melting can occur via a single first-order transition as well as continuously in accordance with the Kosterlitz–Thouless–Halperin–Nelson–Young theory.     

Selections and countably-approachable points

The present paper improves a result of Gutev [V. Gutev, Approaching points by continuous selections, J. Math. Soc. Japan (4) (2006) 1203–1210] by characterizing the countably-approachable points in sense of [V. Gutev, Approaching points by continuous selections, J. Math. Soc. Japan (4) (2006) 1203–1210] by a natural extreme-like condition in the spirit of [V. Gutev, T. Nogura, Vietoris continuous selections and disconnectedness-like properties, Proc. Amer. Math. Soc. 129 (2001) 2809–2815; V. Gutev, T. Nogura, Selection pointwise-maximal spaces, Topology Appl. 146–147 (2005) 397–408]. This demonstrates the natural relationship between different extreme-like points with respect to continuous selections for the Vietoris hyperspace of nonempty closed subsets.