Cient Conditions Research Articles

Convergence of the Discrete Variance Swap in Time-Homogeneous Diffusion Models

In stochastic volatility models based on time-homogeneous diff usions, we provide a simple necessary and sufficient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and Protter (2013) and gives an affirmative answer to a problem posed in this paper in the case of 3/2 stochastic volatility model. We also give precise conditions (not based on asymptotics) when the discrete fair strike of the variance swap is higher than the continuous one and discuss the convex order conjecture proposed by Keller-Ressel and Griessler (2012) in this context.

Concavity of the Consumption Function with Recursive Preferences

Carroll and Kimball (1996) show that the consumption function for an agent with time-separable, isoelastic preferences is concave in the presence of income uncertainty. In this paper I show that concavity breaks down if we abandon time-separability. Namely, if an agent maximizing an isoelastic recursive utility has preferences for early resolution of uncertainty, there always exists a distribution of income risk such that consumption function is not concave in wealth. I also derive sufficient conditions guaranteeing that the consumption function is concave if the agent has preferences for late resolution of uncertainty.

Sufficient conditions for certain subclasses of meromorphic p-valent functions

In the present paper, we obtain certain su¢ cient conditions for meromorphic p-valent functions. Several corollaries and consequences of the main results are also considered.

Some optimization problems on ranks and inertias of matrix-valued functions subject to linear matrix equation restrictions

Matrix rank and inertia optimization problems are a class of dis- continuous optimization problems in which the decision variables are matrices running over certain matrix sets, while the ranks and inertias of the vari- able matrices are taken as integer-valued objective functions. In this paper, we establish a group of explicit formulas for calculating the maximal and minimal values of the rank and inertia objective functions of the Hermitian matrix-valued function A1 B1XB 1 subject to the common Hermitian solu- tion of a pair of consistent matrix equations B2XB 2 = A2 and B3XB 3 = A3, and Hermitian solution of the consistent matrix equation B4X = A4, respec- tively. Many consequences are obtained, in particular, necessary and su- cient conditions are established for the triple matrix equations B1XB 1 = A1, B2XB 2 = A2 and B3XB 3 = A3 to have a common Hermitian solution, as well as necessary and sucient conditions for the two matrix equations B1XB 1 = A1 and B4X = A4 to have a common Hermitian solution.

Existence of positive periodic solutions for higher order singular functional difference equations

We study a higher order singular functional difference equation on Z. Suffi- cient conditions are obtained for the existence of at least one positive periodic solution of the equation. Our proof utilizes the nonlinear alternative of Leray-Schauder.

On the Uniqueness of a Nonlocal Solution in the Barenblatt - Gilman Model

This article deals with the question of uniqueness of a generalized solution to the Dirichlet Cauchy problem for the Barenblatt Gilman equation, which describes nonequilibrium countercurrent capillary impregnation. The unknown function corresponds to e ective saturation. The main equation of this model is nonlinear and implicit with respect to the time derivative, which makes it quite hard to study. In a suitable functional space, the Dirichlet Cauchy problem for the Barenblatt Gilman equation reduces to the Cauchy problem for a quasilinear Sobolev-type equation. Sobolev-type equations constitute a large area of nonclassical equations of mathematical physics. The techniques used in this article originated in the theory of semilinear Sobolev-type equations. For the Cauchy problem we obtain a su cient condition for the existence of a unique generalized solution. We establish the existence of a unique nonlocal generalized solution to the Dirichlet Cauchy problem for the Barenblatt Gilman equation.

Coordinate finite type rotational surfaces in Euclidean spaces

Submanifolds of coordinate finite-type were introduced in [10]. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of ?. In the present study we consider coordinate finite-type surfaces in E4. We give necessary and su_cient conditions for generalized rotation surfaces in E4 to become coordinate finite-type. We also give some special examples.

Recognizing Single-Peaked Preferences on Aggregated Choice Data

Single-Peaked preferences play an important role in the social choice literature. In this paper, we provide necessary and sufficient conditions for observed behaviour to be consistent with a mixture model of single-peaked preferences for a given ordering of the alternatives. These conditions can be tested in time polynomial in the number of choice alternatives. In addition, algorithms are provided which identify the underlying ordering of choice alternatives if ordering is unknown. These algorithms also run in polynomial time, providing an efficient test for the mixture model of single-peaked preferences.

Fishing for Excuses and Performance Evaluation

We study a principal-agent model in which the agent can provide ex post additional relevant information regarding his performance. In particular, he can provide a legitimate excuse, that is, evidence that a poor result is only due to factors outside his control. However, building a convincing case requires time, time that is not spent on exerting productive eff ort, and thus generating information represents an opportunity cost. We obtain necessary and suffi cient conditions for the principal to prefer a policy of adjusting ex post the performance measure for the information provided by the agent to a policy of conforming to a result-based system with no adjustments. The risk aversion and a possible limited liability of the agent play an important role in the analysis. This paper clarifi es the issues asso- ciated with the so-called \excuse culture prevailing in some organizations.

A note on the existence of the maximum likelihood estimate in variance components models

In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhya 61, 1999), giving a necessary and suffi- cient condition for the existence of the maximum likelihood estimate in this model, are pointed out and corrected. A new proof of Theorem 3.4 in the Demidenko and Massam's article, concerning the existence of the REML estimate of variance components, is presented.

A MISCELLANY OF SELECTION THEOREMS WITHOUT CONVEXITY

Abstract. In this paper, we give sucient conditions for a mapwith nonconvex values to have a continuous selection and the se-lection extension property in LC-metric spaces under the one-pointextension property. And we apply it to weakly lower semicontinu-ous maps and generalize previous results. We also get a continuousselection theorem for almost lower semicontinuous maps with closedsub-admissible values in R-trees. 1. IntroductionIn 1956, Michael [13] stated the important and well-known selectiontheorem;Theorem 1.1. Let Xbe a paracompact space, Ybe a Banach space,and F : X ( Y be a lower semicontinuous map with closed convexvalues. Then Fhas a continuous selection; that is, there is a continuousfunction f: X!Y such that f(x) 2F(x) for all x2X.Michael???s selection theorem has been extended to spaces with a gen-eralized de nition of convexity and maps with a weaker notion of lowersemicontinuity. The following selection theorems are examples of suchresults in LC-metric spaces, hyperconvex spaces and R-trees;Theorem 1.2. (Gutev [5]) Let Xbe a paracompact space, Y be aBanach space, and F: X( Y be a weakly lower semicontinuous mapwith closed convex values. then Fhas a continuous selection.

INTERVAL-VALUED FUZZY SUBGROUPS

We study the conditions under which a given interval-valued fuzzy subgroup of a given group can or can not be realized as a union of two interval-valued fuzzy proper subgroups. Moreover, we provide a simple necessary and su cient condition for the unio of an arbitrary family of interval-valued fuzzy subgroups to be an interval-valued fuzzy subgroup. Also we formulate the concept of interval-valued fuzzy subgroup generated by a given interval-valued fuzzy set by level subgroups. Furthermore we give characterizations of interval-valued fuzzy conjugate subgroups and interval-valued fuzzy characteristic subgroups by their level subgroups. Also we investigate the level subgroups of the homomorphic image of a given interval-valued fuzzy subgroup.

Pareto Optimal Allocations and Optimal Risk Sharing for Quasiconvex Risk Measures

Pareto optimal allocations and optimal risk sharing for coherent or convex risk measures as well as for insurance prices have been studied widely in the literature. In particular, Pareto optimal allocations have been characterized by applying inf-convolution of risk measures and convex analysis. In the recent literature, an increasing interest has been devoted to quasiconvex risk measures, that is risk measures where convexity is replaced by quasiconvexity and cash-additivity is dropped. The main goal of this paper is then to generalize the characterization of Pareto optimal allocations known for convex risk measures (see, among others, Jouini et al.) to the quasiconvex case. Following the approach of Jouini et al. for convex risk measures, in the quasiconvex case we provide sucient conditions for allocations to be (weakly) Pareto optimal in terms of exactness of the so-called quasiconvex inf-convolution. Moreover, we give a necessary condition for weakly optimal risk sharing that is also sucient under cash-additivity of at least one between the risk measures.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE SOLVABILITY AND MAXIMAL REGULARITY OF ABSTRACT DIFFERENTIAL EQUATIONS OF MIXED TYPE IN HÖLDER SPACES

In this paper we study and obtain some necessary and su¢ cient conditions on the data for the existence, uniqueness of the strict solution and maximal regularity for some second-order dierential equations with mixed boundary conditions whose forcing term belongs to Holder continu- ous spaces. A few illustrative examples related to the interpolation theory are discussed. Key Words and Phrases. Second order abstract dierential equa- tion, Boundary condition, Analytic semigroup, Maximal regularity, Ellip- tic equation, Holder spaces, Square root of operator. 2000 Mathematics Subject Classi…cation Numbers. 34G10, 34K10, 35J25, 47D03.

POSET METRICS ADMITTING ASSOCIATION SCHEMES AND A NEW PROOF OF MACWILLIAMS IDENTITY

It is known that being hierarchical is a necessary and suffi- cient condition for a poset to admit MacWilliams identity. In this paper, we completely characterize the structures of posets which have an associ- ation scheme structure whose relations are indexed by the poset distance between the points in the space. We also derive an explicit formula for the eigenmatrices of association schemes induced by such posets. By using the result of Delsarte which generalizes the MacWilliams identity for linear codes, we give a new proof of the MacWilliams identity for hierarchical linear poset codes.

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

2-Dimensional Reversible Hexagonal Cellular Automata with Periodic Boundary

The hexagonal nite cellular automata (shortly HFCA) are 2-dimensional (2D) cellular automata whose cells are of the form of hexagonal. Morita et al. [1] introduced this type of cellular automaton (CA) and they called it hexagonal partitioned CA (HPCA). A remarkable application of the family of these CAs is presented by Trun o [2] where a model is presented to simulate the evolution of forest res and Hernandez Encinas et al. [3] where they introduce a new mathematical model for predicting the spread of a re front in homogeneous and inhomogeneous environments. Also, in [4], debris ows are simulated and modeled by two-dimensional hexagonal cellular automata. These families of cellular automata are also applied to design discrete models of chemical reaction-di usion systems [5]. Also, 2D CAs have found applications in tra c modeling. For instance multi-value (including ternary) CA models for tra c ow are proposed in [6]. Recently, cellular automata have found applications in cryptography [7, 8], especially 2D CA have been proposed for multi-secret sharing scheme for colored images [9]. Due to the applications and modeling on hexagonal cellular automata, the algebraic structure of cellular automata has been of much interest to the researchers [10 13]. Algebraic representation of 2D CA helps in determining the characterization of CA. An important characterization is the determination of the reversibility of CA [13]. In [14], we have characterized a 2D nite CA by using matrix algebra built on Z3. Also, we have analyzed some results about the rule numbers 2460N and 2460P. In [15], we have obtained necessary and su cient conditions for the existence of Garden of Eden con gurations for 2D ternary CAs. In this paper, we deal with CA de ned by hexagonal rules under periodic boundary condition (PBC) and the ternary eld Z3. We obtain the rule matrix of the hexagonal nite periodic cellular automaton (HFPCA). We compute the rank of rule matrices related to HFPCA via an algorithm. Hence, we determine the reversibility of this type 2D CA which is one of the di cult problems in higher dimension as explained in the previous paragraph. Further, by using the matrix algebra it is shown that the HFPCA are reversible, if the number of columns is even and the HFPCA are not reversible, if the number of the columns is odd. A periodic boundary CA is the one where the extreme cells in the boundaries are adjacent to each other periodically [16]. A null boundary CA is the one where the extreme cells in the boundaries are connected to the zero states. The surrounding cells are all in zero state. For convenience of analysis, the state of each cell is an element of a nite or in nite state set. Moreover, the state of the cell (i, j) at time t is denoted by x (t) (i,j). The state of the cell (i, j) at time t+1 is denoted by x (t+1) (i,j) = y (t) (i,j). Let us consider the

Weak ergodicity of nonhomogeneous Markov chains on noncommutative $L^1$-spaces

In this paper we study certain properties of Dobrushin's ergod- icity coe�cient for stochastic operators de�ned on noncommutative L 1 -spaces associated with semi-�nite von Neumann algebras. Such results extends the well-known classical ones to a noncommutative setting. This allows us to in- vestigate the weak ergodicity of nonhomogeneous discrete Markov processes (NDMP) by means of the ergodicity coe�cient. We provide a su�cient condi- tions for such processes to satisfy the weak ergodicity. Moreover, a necessary and su�cient condition is given for the satisfaction of the L 1 -weak ergodicity of NDMP. It is also provided an example showing that L 1 -weak ergodicity is weaker that weak ergodicity. We applied the main results to several concrete examples of noncommutative NDMP.

Kaczmarz algorithm with relaxation in Hilbert space

We study the relaxed Kaczmarz algorithm in Hilbert space. The connection with non relaxed algorithm is examined. In particular we give su cient conditions when relaxation leads to the convergence of the algorithm independently of the relaxation coe cients.

On Psi-conditional asymptotic stability of first order nonlinear matrix Lyapunov system

We provide necessary and sucient conditions for psi-conditional as-ymptotic stability of the solution of a linear matrix Lyapunov system and sucientconditions for psi -conditional asymptotic stability of the solution of a rst ordernon-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).