Bilateral gamma distributions and processes in financial mathematics

We present a class of Lévy processes for modelling financial market fluctuations: bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated Lévy processes. We treat exponential Lévy stock models with an underlying bilateral Gamma process as well as term structure models driven by bilateral Gamma processes, and apply our results to a set of real financial data (DAX 1996–1998).     

Bilateral comparisons and consistent fair division rules in the context of bankruptcy problems

We analyze the problem of extending a given bilateral principle of justice to a consistentn-creditor bankruptcy rule. Based on the bilateral principle, we build a family of binary relations on the set of creditors in order to make bilateral comparisons between them. We find that the possibility of extending a specific bilateral principle of justice in a consistent way is closely related to the quasi-transitivity of the binary relations mentioned above.     

Stakeholder bargaining games

We study bilateral bargaining problems with an interested third party, the stakeholder, that enjoys benefits upon a bilateral agreement. To address the strategic implications of stakeholders over negotiations, we consider a model where two bargainers interact in the presence of a third party that (a) can transfer a share of her benefits to the bargainers but cannot receive a share of the bilateral surplus, and (b) while she may not participate in all periods of the negotiation, she cannot remain entirely inhibited. Our main findings are:(1) the stakeholder’s (reverse) liquidity constraint implies the existence of a multiplicity of stationary subgame perfect equilibria that include outcomes with very asymmetric bilateral agreements, and (2) the partial participation of the stakeholder may be the source of severe inefficiency     

<Emphasis Type="Italic">q</Emphasis>-extensions of Dougall’s bilateral <Subscript>2</Subscript>H<Subscript>2</Subscript>-series

Transformations for a bilateral ₂ ψ ₂-series are investigated by means of Abel’s lemma on summation by parts. Two q-extensions of Dougall’s classical identity for bilateral ₂H₂-sum are established. As by-products, the Rogers–Fine identity is recovered and a new proof is presented for Bailey’s identity of bilateral well-poised ₆ ψ ₆-series.     

The Saalschütz chain reactions and bilateral basic hypergeometric series

By iterating recursively the q-Saalschütz summation formula, we introduce the Saalschütz chain reactions. A general series transform, which expresses a nonterminating bilateral series in terms of a finite multiple unilateral sum, will be established. As applications we derive, by means of Bailey’s 6ψ6 -series identity, several bilateral transformations including one due to Milne [12]. These transformations further yield a number of closed formulas of very well-poised bilateral basic hypergeometric series; which are closely related to the identities obtained by Minton [13], Karlsson [11], Gasper [8], and Chu [5], [6], [7] through the partial fraction method and divided differences.     

On Aronsson Equation and Deterministic Optimal Control

When Hamiltonians are nonsmooth, we define viscosity solutions of the Aronsson equation and prove that value functions of the corresponding deterministic optimal control problems are solutions if they are bilateral viscosity solutions of the Hamilton-Jacobi-Bellman equation. We characterize such a property in several ways, in particular it follows that a value function which is an absolute minimizer is a bilateral viscosity solution of the HJB equation and these two properties are often equivalent. We also determine that bilateral solutions of HJB equations are unique among absolute minimizers with prescribed boundary conditions. This research was partially supported by MIUR-Prin project “Metodi di viscosità, metrici e di teoria del controllo in equazioni alle derivate parziali nonlineari”.     

马氏调制强度的传染模型下CDS的CVA计算

本文考虑了具有马氏调制强度的传染模型下,信用违约互换(CDS)的双边信用估值调整(CVA).在我们考虑的模型中,利率、回收率以及CDS的买方、卖方和参照实体三方的违约强度均受宏观经济环境的影响,该经济状况由一连续时间状态的齐次马氏链所刻画.利用测度变换和累积强度的Laplace变换,我们给出了CDS合同的双边CVA的表达公式,该公式可以表示为线性常微分方程组的基本解的形式.利用所得到的公式,我们数值分析了马氏调制和违约相关性对双边CVA的影响.     

On tests of hypotheses about treatment effects and treatmentX places interactions,in two heteroscedastic experiments

Summary Suppose we have two independent experiments conducted with a set of ‘t’ treatments each, at different places. This paper deals with two interesting problems of testing of hypotheses associated with these experiments. The first problem deals with the test of the equality of the respective treatment effects in the two experiments. The second problem is concerned with the testing of the equality of treatment into places interactions. Though we assume normality, the variance σ ₁ ² in one experiment is assumed different from the variance σ ₂ ² in the other experiment. When no information is available aboutR=σ ₁ ² /(σ ₁ ² +σ ₂ ² ) except that 0≦R≦1, tests known as ‘bilateral tests’ are proposed in the literature, to test the hypotheses mentioned above. This paper studies some important small sample properties of these bilateral tests. More specifically we study the probability of the first and second kind of error of these bilateral tests as a function ofR. When the two experiments have the same number of observations on each treatment, the bilateral test is shown to control the first kind of error. Fort=1,2, the level of these tests is a strictly convex function ofR and hence these tests can be very conservative. Some power properties of these tests are also obtained. Two tests which are equivalent to the bilateral tests for large sample sizes, and which are superior to the bilateral tests for small sample sizes, are obtained.     

Bilateral analog of the Newton method for determination of eigenvalues of nonlinear spectral problems

The iterative algorithm for determination of bilateral (alternating) approximations to the eigenvalues of nonlinear spectral problems that uses a bilateral analog of the Newton method and a new efficient numerical procedure for calculation of the Newton correction and its derivative is proposed. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 65–73, January–March, 2008.     

The homogeneous shifts

A bounded linear operator T on a complex Hilbert space is called homogeneous if the spectrum of T is contained in the closed unit disc and all bi-holomorphic automorphisms of this disc lift to automorphisms of the operator modulo unitary equivalence. We prove that all the irreducible homogeneous operators are block shifts. Therefore, as a first step in classifying all of them, it is natural to begin with the homogeneous scalar shifts.In this paper we determine all the homogeneous (scalar) weighted shifts. They consist of the unweighted bilateral shift, two one-parameter families of unilateral shifts (adjoints of each other), a one-parameter family of bilateral shifts and a two-parameter family of bilateral shifts. This classification is obtained by a careful analysis of the possibilities for the projective representation of the Möbius group associated with an irreducible homogeneous shift.     

Farsighted free trade networks

The paper examines whether bilateral free trade agreements can lead to global free trade. We reconsider the endogenous tariff model introduced by Goyal and Joshi (2006) who study pairwise stability of free trade networks. We depart from their analysis by adopting the concept of pairwise farsightedly stable networks (Herings et al. 2009, GEB). We show that the complete network (i.e., global free trade) constitutes a pairwise farsightedly stable set. In particular, there is a farsightedly improving path from the empty network (i.e., no free trade agreement in place) to the complete network, which involves link additions only, while farsightedly improving paths from preexisting free trade networks may involve link deletion (i.e., dissolution of some bilateral FTAs). Moreover, we show that pairwise farsightedly stable set of networks is not unique. One implication of our results is that bilateral trade negotiations, if properly channeled, can lead to global free trade, although some bilateral agreements may have to be dissolved first to pave the way towards global free trade.     

M. Jackson’s bilateral 3 H 3-series and extension with integer parameters

A general transformation theorem is proved between nonterminating bilateral _λ+3 H _3+λ -series. By applying it to M. Jackson’s ₃ H ₃-series, we then derive five bilateral summation formulae as consequences.     

Global probability maximization for a Gaussian bilateral inequality in polynomial time

The present paper investigates Gaussian bilateral inequalities in view of solving related probability maximization problems. Since the function f representing the probability of satisfaction of a given Gaussian bilateral inequality is not concave everywhere, we first state and prove a necessary and sufficient condition for negative semi-definiteness of the Hessian. Then, the (nonconvex) problem of globally maximizing f over a given polyhedron in \(\mathbb {R}^{n}\) is adressed, and shown to be polynomial-time solvable, thus yielding a new-comer to the (short) list of nonconvex global optimization problems which can be solved exactly in polynomial time. Application to computing upper bounds to the maximum joint probability of satisfaction of a set of m independent Gaussian bilateral inequalities is discussed and computational results are reported.     

Spectrum of bilateral shifts with operator-valued weights

We describe the spectrum of bilateral operator-weighted shifts.

     

A characterization of bilateral operator weighted shifts being Cowen-Douglas operators

It is characterized when a bilateral operator weighted shift is a Cowen-Douglas operator.

     

美国经济冲击对东亚经济波动的传导:基于面板logit模型的实证分析

美国经济冲击会通过具体渠道进行传导,影响东亚地区的经济波动.具体来看,与美国的双边进口贸易渠道和FDI渠道的传导会增加东亚地区经济波动概率,并且在控制国内经济规模后,边际效应进一步提高;与美国的双边出口贸易渠道和汇率渠道的传导反而会降低东亚地区经济波动的概率;并且传导效应在不同经济发展程度的国家呈现出明显的差异,发展中经济体受美国经济冲击的影响较大.     

On a Steffensen-Hermite method of order three

In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the Hermite inverse interpolation polynomial of degree 2. We study the convergence of the iterative method and we provide new convergence conditions which lead to bilateral approximations for the solution; it is known that the bilateral approximations have the advantage of offering a posteriori bounds of the errors. The numerical examples confirm the advantage of considering these error bounds.     

Two new transformation formulas of basic hypergeometric series

By means of a modified version of Cauchy's method for obtaining bilateral series identities, two new transformation formulas for bilateral basic hypergeometric series are derived. These contain several important identities for basic hypergeometric series as special cases, including the nonterminating q-Saalschütz summation, Bailey's very well-poised summation and the nonterminating Watson transformation.     

Modeling of the Crosstalk Phenomenon by Bilateral Coupling of the Non-Stationary Maxwell Equations and the Circuit Equations

In this paper, we introduce a general modeling approach for the crosstalk phenomenon within electro-magnetic systems. We model the phenomenon by bilateral coupling of two sets of differential equations, namely non-stationary Maxwell equations and circuit equations. Considering these two sets of equations as input-output systems, the bilateral coupling approach connects the output of one system to the input of the other system and conversely, via coupling and re-coupling relations. The coupling of these two sets leads to a set of partial differential-algebraic equations modeling the crosstalk phenomenon. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

双边市场异业合作网络平台的定价策略

本文以网络平台异业合作为背景,在Hotelling模型框架下,基于双边用户都是部分多归属的假定,结合平台采取异业合作可以提高用户固有收益这一前提,分析了产品和服务的差异化程度、拥挤效应及组间网络外部性强度对网络平台定价策略的影响。结果显示,双边用户的组间网络外部性强度不同时,随着拥挤效应的增强或产品和服务的差异化程度的提高,无论是在位平台还是采取异业合作的新进入平台,都会对一边用户提高,而对另一边用户降低收取的交易费;组间网络外部性强度相同时,平台对双边用户收取的交易费相同,且只与用户固有收益及交易量有关。研究表明,新进入市场的网络平台不应采取传统双边市场中常用的价格战策略来争夺市场份额,而应积极采取异业合作,通过提供优质优价的产品和服务来同在位平台竞争。