Comparison of the performance of a time‐dependent short‐interest rate model with time‐independent models

The coefficients in the stochastic differential equation that the short interest rate follows are of vital importance in the subsequent modelling of bond prices and other interest rate products. Empirical tests have previously been performed by various authors who compare a variety of popular short‐rate models. Most recently, Ahn and Gao compared their model with affine‐drift models and showed that their model with a non‐linear drift function outperforms the others. This paper compares the model developed by Goard, which is a time‐dependent generalization of the Ahn–Gao model, with the Ahn–Gao model itself. It is found that the time‐dependent model using a second‐order Fourier series in time, outperforms the Ahn–Gao model for all data sets considered.     

On Statistical Properties of the Lerch Zeta‐Function

A discrete limit theorem for the Lerch zetafunction on the complex plane is proved.     

Divisibility in the K0‐Group of the Algebra of Operators on a Banach Space

Let Figiel's reflexive Banach space which is not isomorphic to its Cartesian square. We show that the K ₀group of the algebra of continuous, linear operators on contain a subgroup isomorphic to the group c ₀₀( ) of sequences rational numbers with z _n=0 eventually.     

On the Ordered K0‐Group of Universal, Free Product C*‐Algebras

The ordered K₀-group of the universal, unital free product C^*-algebra M_k()*M_l()is calculated in the case where k is prime and not a divisor in l. It is shown that the positive cone of K₀(M_k()*M_l())is as small as possible in this case. The article also contains results (full and partial) on the ordered K₀0-group of more general universal, unital free product C^* algebras.     

Modelling the Temperature Time‐dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing

In this paper, in the context of an Ornstein–Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non‐parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent.     

Error analysis of upwind‐discretizations for the steady‐state incompressible Navier–Stokes equations

Within the framework of finite element methods, the paper investigates a general approximation technique for the nonlinear convective term of the Navier–Stokes equations. The approach is based on an upwind method of finite volume type. It is proved that the discrete convective term satisfies a well‐known collection of sufficient conditions for convergence of the finite element solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Critique of probabilistic models: Application of the Semi‐Markov model to migration

The role of probabilistic models, with special reference to application of the Semi‐Markov model to the analysis of internal migration, is discussed. Advantages of probabilistic models over more conventional methods based on regression analysis are detailed. Probabilistic models have stood apart from the rest of the literature, in migration as well as other areas of application, because they have no substantive content. It is argued that unless their parameters are related to the causal structure and exogenous determinants of the migration process, probabilistic models will be of little practical and scientific use. A strategy for integrating probabilistic models with theoretical and empirical analysis is sketched, to be carried out in the next article.     

A comparison of the alpha‐ and beta‐characteristic functions in cooperative non‐sidepayment n‐person games 1

This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Results are interpreted as showing that β‐effectiveness is superior to a‐effectiveness as a basis for payoff predictions in cooperative non‐sidepayment games.     

A Discrete Limit Theorem for the Matsumoto Zeta‐Function in the Space of Meromorphic Functions

In the paper, a discrete limit theorem for the Matsumoto zetafunction in the space of meromorphic functions is proved.     

A Discrete Limit Theorem for the Matsumoto Zeta‐Function in the Space of Analytic Functions

In the paper, a discrete distribution of the Matsumoto zetafunction is considered. It is proved that the probability measure , converges weakly as .     

Modelling the trade‐offs between farm income and the reduction of erosion and nitrate pollution

Water is a very limited resource in Tunisia, both in quantity and in quality. Problems of quality are related to urban, industrial and agricultural activity. Erosion is causing dams to silt up and is leading to phosphorus accumulation in water. The use of agrochemicals, primarily nitrogen and phosphorus, is causing problems of eutrophication. This paper presents the results of a study of sediment and nitrate pollution. The methodology used is based on the EPIC simulation model and a multiobjective programming model (MOPM). The data generated by EPIC are input for the MOPM together with the economic variables. These tools are applied to a 486 ha farm located in northern Tunisia which includes an irrigated area of 300 ha. The study considers three objectives: maximization of gross margin, minimization of erosion, and minimization of nitrate losses. The noninferior set estimation method is implemented to generate the tradeoff curves between the objectives. Results show that nitrate losses are important for both rainfed and irrigated land. The same conclusion is valid for erosion. It is shown that the farmer can reduce the environmental burden without decreasing gross margin, since he is operating below the efficiency curve.     

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.     

Contributions to the theory of first‐exit times of some compound processes in queueing theory

We consider compound processes that are linear with constant slope between i.i.d. jumps at time points forming a renewal process. These processes are basic in queueing, dam and risk theory. For positive and for negative slope we derive the distribution of the first crossing time of a prespecified level. The related problem of busy periods of single‐server queueing systems is also studied. This revised version was published online in June 2006 with corrections to the Cover Date.     

A structural model of the higher‐order Markov process incorporating reversion effects

The paper presents a formal approach which may increase the realism and parsimony of higher‐order Markov models applied to certain human behaviors. Often in behavioral applications, any improvements in fit available from increasing the order of a Markov model would be more than offset by interpretive problems caused by the very rapid increase in the number of independent parameters. The model proposed here for the higher‐order process greatly reduces the number of independent parameters, replacing them with sociologically relevant effects of persistence in and reversion to previous conditions.

The general model is called the “reversion model.” In it, individuals are allowed to carry along some information about their pasts, for a number of periods corresponding to the order of the model. The parameters describing residence histories are constructed to give each individual an underlying set of first‐order transition probabilities, which are modified by experience of the various states of the system. When an individual occupies a particular state, his relative probability of future residence there (vis‐a‐vis the other states as a group) is permitted to change. But occupation of a particular state is not permitted to affect the relative chances of residence among the other states. With suitable constraints, the number of parameters of this higher‐order process no longer increases geometrically with the order, but only arithmetically.

Maximum likelihood estimation formulas are derived for the reversion model, which is then applied to longitudinal data on the work activities of U.S. Ph.D. physicists and chemists in 1960–1966, and is found to fit well using likelihood ratio tests.     

Economic and biological risk analysis of the Norwegian spring‐spawning herring fishery

The purpose of this paper is to study the biological and economic risks involved in the management of the Norwegian springspawning herring fishery. We use a discrete time and agestructured model based on historical data. The current paper investigates, under different levels of fishing mortalities, the risk probabilities related to the time behaviour of the spawning stock and profit. We show that the exploitation of the herring stock is vulnerable to small changes in harvesting and price level.     

Effect of non‐normality on the power in analysis of variance: A simulation study

The use of simulation methods for calculating the power values in the case of non‐normal errors is discussed. One and two‐way layouts are considered for the fixed effect model. The Erlangian and contaminated normal distribution are taken as examples of a non‐normal error distribution. The results obtained by these methods are given in tables 1 and 2 which indicate that for inference concerning means the power calculated under normal theory is only slightly affected by the non‐normality of the errors.     

A graph theoretic approach to the investigation of system‐environment relationships†

For any empirical structure consisting of a system S and its environment E, there is an associated digraph D whose points and arcs (directed lines) correspond to the elements and relationships of the structure. The arcs of D are thus of four types: (1) internal arcs, which join two points of S; (b) external arcs, which join two points of E; (c) out‐liaisons of S, which join a point of S to one of E; and (d) in‐liaisons of S, which join a point of E to one of S. The boundary of S is defined as the subgraph of D induced by the liaisons of S and corresponds to those elements and relationships of the structure directly involved in transactions between the system and its environment. The basic structural properties of boundaries are then identified, and it is shown how the points of S and E can be stratified according to their distances to (or from) the boundary of S. Next, several results are derived concerning system‐environment relationships in structures whose digraphs are symmetric, transitive, or signed. The concept of convexity is then introduced to deal with a certain kind of segregation of a system relative to its environment. And, finally, it is shown how the adjacency matrix of D can be employed to facilitate the analysis of such structures and the calculation of various indexes of system‐environment relationships.     

On Small Values of the Riemann Zeta‐Function on the Critical Line and Gaps Between Zeros

Small values of are investigated, using the value distribution results of A. Selberg. This gives an asymptotic formula for Some related problems involving values of and gaps between ordinates of consecutive zeros of (s) are also discussed.     

A Course of Statistical Treatment of Experimental Data for Technical People with the Use of a Time‐Sharing Digital Computer in the Classroom

After a short examination of the problem of training in industry with the aim of integrating the knowledge of young scientists and technical people, and of overcoming the obsolescence of personnel charged with technical work, this paper stresses the importance of the statistical treatment of experimental data. The paper describes the programme of a course on this subject, developed through the extensive use of a time‐sharing digital computer with a terminal in the classroom: the computer being programmed to simulate sources of experimental results and to verify the essential theorems of statistics.     

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.