Minimizing coherent risk measures of shortfall in discrete‐time models with cone constraints

The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete‐time financial models with cone‐constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super‐hedging a contingent claim, which is represented as a Neyman–Pearson‐type random variable.     

Multi‐asset barrier options and occupation time derivatives

A general framework is formulated to price various forms of European style multi‐asset barrier options and occupation time derivatives with one state variable having the barrier feature. Based on the lognormal assumption of asset price processes, the splitting direction technique is developed for deriving the joint density functions of multi‐variate terminal asset prices with provision for single or double barriers on one of the state variables. A systematic procedure is illustrated whereby multi‐asset option price formulas can be deduced in a systematic manner as extensions from those of their one‐asset counterparts. The formulation has been applied successfully to derive the analytic price formulas of multi‐asset options with external two‐sided barriers and sequential barriers, multi‐asset step options and delayed barrier options. The successful numerical implementation of these price formulas is demonstrated.     

A two‐step procedure for clustering time varying data

The aim of this paper is to enlarge the usual domain of cluster analysis. A procedure for clustering time varying data is presented which takes into account the time dimension with its intrinsic properties.

This procedure consists of two steps. In the first step a dissimilarity between variables is defined and the dissimilarity matrix is calculated for each unit separately. In the second step the dissimilarity between units is calculated in terms of the dissimilarity matrices defined in the first step. The dissimilarity matrix obtained is the base for a suitable clustering method.

The procedure is illustrated on an empirical example.     

Finite‐dimensional Realizations of Regime‐switching HJM Models

This paper studies Heath–Jarrow–Morton‐type models with regime‐switching stochastic volatility. In this setting the forward rate volatility is allowed to depend on the current forward rate curve as well as on a continuous time Markov chain y with finitely many states. Employing the framework developed by Björk and Svensson we find necessary and sufficient conditions on the volatility guaranteeing the representation of the forward rate process by a finite‐dimensional Markovian state space model. These conditions allow us to investigate regime‐switching generalizations of some well‐known models such as those by Ho–Lee, Hull–White, and Cox–Ingersoll–Ross.     

On a McKean‐Vlasov Stochastic Integro‐differential Evolution Equation of Sobolev‐Type

Abstract

We establish the global existence and uniqueness of mild solutions for a class of first‐order abstract stochastic Sobolev‐type integro‐differential equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time, t, but also on the corresponding probability distribution at time t. Results concerning the continuous dependence of solutions on the initial data and almost sure exponential stability, as well as an extension of the existence result to the case in which the classical initial condition is replaced by a so‐called nonlocal initial condition, are also discussed. Finally, an example is provided to illustrate the applicability of the general theory.     

Asymptotic convergence of degree‐raising

It is well known that the degree‐raised Bernstein–Bézier coefficients of degree n of a polynomial g converge to g at the rate 1/n. In this paper we consider the polynomial A _n(g) of degree ⩼ n interpolating the coefficients. We show how A _n can be viewed as an inverse to the Bernstein polynomial operator and that the derivatives A _n(g)(^r) converge uniformly to g(^r) at the rate 1/n for all r. We also give an asymptotic expansion of Voronovskaya type for A _n(g) and discuss some shape preserving properties of this polynomial. This revised version was published online in June 2006 with corrections to the Cover Date.     

Large time behavior of Euler-Poisson system for semiconductor

In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.     

The multiple server effect: Optimal allocation of servers to stations with different service‐time distributions in tandem queueing networks

Traditionally, studies on tandem queueing networks concentrate on systems with infinite buffers, exponential service times, and/or single servers where solutions are more tractable. Less research can be found on more general, less tractable systems. We examine multipleserver systems with finite buffers and nonexponential service times, studying the effects of coefficient of variation (cv) of the servicetime distribution on the throughput of these systems, where cv differs among stations.Starting with the single station, we examine the effects of cv and the number of servers at the station on the distribution of interdeparture times. This insight helps explain the differences in throughput seen in the single (fast) server vs. multiple (slow) server problem. These results, in turn, shed light on the server allocation problem when cv differs among stations. We present some observations, as well as the intuition behind them.     

Understanding secondary mathematics: analysis of linguistic difficulties vis‐a‐vis errors

Misconceptions caused by misunderstanding mathematical language are of different types, e.g. interference of mathematical and non‐mathematical meanings, complexity or unfamiliarity of words, improper use of symbols, syntactical misunderstandings and redundancy or inadequacy of data. Fifteen mathematical words were presented to 84 students of 8th grade and the responses of students were analysed. Mathematical items of a Science Talent Search Test were also analysed from the answers of 100 candidates of 8th grade. The analysis casts light on the processes of the development of mathematical concepts which the students learn through the vicissitudes of the interaction of mathematical and non‐mathematical meanings of words which may be familiar or unfamiliar, relevant or irrelevant, and/or distinct or difficult, to the learners. Complications in understanding mathematical concepts for individual students are pointed out from these experiments. Acquaintance with such communication processes of learners can also help in detecting strategies of imparting mathematical instructions to the learners. Roles of the uses of common, mathematical, transformational, and story‐telling language have also been discussed. The paper concludes with some comments on the importance of guided discovery learning, error analysis by teachers, and the preparation of a register of mathematical language.     

Exponential time integration of solitary waves of cubic Schrödinger equation

The aim of the present paper is to study the suitability of using exponential methods for the time integration of cubic Schrödinger equation till long times. We center on second-order methods, for which we prove a higher order of accuracy on the main invariants when integrating solitary waves. Some geometric implicit exponential methods are considered as well as some explicit suitably projected ones. The comparison in terms of efficiency is performed.     

Energy identity of the heat flow of H-systems at finite singular time

It is well known that there exists a global solution to the heat flow of H-systems.If the solution satisfies a certain energy inequality,it is global regular with at most finitely many singularities. Under the same energy inequality,we can show the energy identity of the heat flow of H-systems at finite singular time.The most interesting thing in our proof is that we find the singular points can only occur in the interior of the set in some sense.     

On the Completeness and Decidability of the Horn‐Like Fragment of the First‐Order Linear Temporal Logic

We prove the completeness and decidability of the Hornlike sequents, specifically, the socalled D₂sequents (of the firstorder linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus G_L, grounded by the author in his earlier papers, for D₂sequents we construct a D₂Sat calculus of the socalled saturated type consisting of decidable deductive procedures replacing the omegarule for the always operator. In the present paper, in order to prove the completeness and decidability of the calculus D₂Sat, we construct the socalled invariant decidable calculus D₂IN. We prove the equivalence of the calculi D₂IN, D₂Sat, and G _L ^** for the socalled saturated D₂sequents. From this equivalence, by reducing an arbitrary D₂sequent to a saturated D₂sequent, and also from the completeness of the G _L ^** calculus and decidability of the invariant calculus D₂IN, we deduce the completeness and decidability of the calculus D₂Sat in the class of D₂sequents.     

Stability of a three‐station fluid network

This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline. This revised version was published online in June 2006 with corrections to the Cover Date.     

Parameterization of m‐channel orthogonal multifilter banks

A complete parameterization for the m‐channel FIR orthogonal multifilter banks is provided based on the lattice structure of the paraunitary systems. Two forms of complete factorization of the m‐channel FIR orthogonal multifilter banks for symmetric/antisymmetric scaling functions and multiwavelets with the same symmetric center (1 + γ + γ/(m - 1)) for some nonnegative integer γ are obtained. For the case of multiplicity 2 and dilation factor m = 2, the result of the factorization shows that if the scaling function Φ and multiwavelet Ψ are symmetric/antisymmetric about the same symmetric center γ + for some nonnegative integer γ, then one of the components of Φ (respectively Ψ) is symmetric and the other is antisymmetric. Two examples of the construction of symmetric/antisymmetric orthogonal multiwavelets of multiplicity 3 with dilation factor 2 and multiplicity 2 with dilation factor 3 are presented to demonstrate the use of these parameterizations of orthogonal multifilter banks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Competitiveness of biomass‐fueled electrical power plants

One way countries like the United States can comply with suggested rollbacks in greenhouse gas emissions is by employing power plants fueled with biomass. We examine the competitiveness of biomassbased fuel for electrical power as opposed to coal using a mathematical programming structure. We consider fueling power plants from milling residues, whole trees, logging residues, switch grass, or shortrotation woody crops. We do this using a combined model of the agricultural and forestry sectors. We find that the competitiveness of biomass depends in a key way upon the success of research in developing improved production methods for shortrotation woody crops without great increases in costs.     

Asymptotic behaviour of dynamic systems on time scales†

This paper is concerned with asymptotic behaviour of solutions of perturbed dynamic systems on time scales. A time scale version of the Hartman–Wintner theorem is established for a class of time scales.     

On conjugate complex time—I: complex time implies existence of tangential potential that can cause some equipotential effects of gravity

El Naschie's idea of complex time implies the possibility of spatial decomposition of rate of time flow that does not lead to the unphysical consequences for which those former attempts at multidimensional time have been criticized. The spatial decomposition of time rate suggests a spatial decomposition of energy which in turn would require presence of certain tangential component of a generalized vector potential, whether gravitational or electromagnetic. Existence of the new tangential potential could explain the observed frequency decrease of radio signals as well as the apparent anomalous radial acceleration towards the sun that was found in the case of the “runaway” spacecrafts Pioneer 10 and 11. The spatial decomposition of time rate dismisses any possibility of travel back in time and thus prohibits any acausal happenings due to reversal of time flow.