Deterministic macroeconomic dynamic equations from a stochastic microeconomic description: The role of time scales

In the present paper, we develop the ‘stochastic’ microeconomic approach to obtained a deterministic macrodynamic equation. Three time scales have to be introduced. To be valid, the dynamic equation has to be written on the meso-scopic time scale. ‘Discrete’ and ‘continuous’ time versions are given. On the other hand, the comparison between the ‘stochastic’ and the ‘average’ (all the agents have the same characteristics, the ‘average’ ones) approaches is presented. Both methods give the same form for the dynamic equation, nevertheless the ‘average’ approach gives conditions of validity which are not strict enough. An advantage of the ‘stochastic’ approach is to inforce this point and to propose a better framework for writing down deterministic macrodynamic equations and for making further developments if necessary.     

Classification of Gaussian random processes using a simple linear discriminant and its application to seismic differentiation

A regression solution is adopted for the problem of discrimination between Gaussian random processes (time series). This has led to the introduction of a simple but ‘efficient’ linear discriminant. The application to actual practice is demonstrated by consideration of the important problem of explosion-earthquake differentiation.     

Stability of jurisdiction structures in economies with local public goods

Individuals of different types can form groups, i.e. jurisdictions, for the purposes of collective consumption and production of local public goods by the members of the jurisdictions. Also, the utility of an individual may be affected by the composition and size of the jurisdiction of which he is a member. Jurisdiction formation is endogenous. Trade of private goods can occur within jurisdictions and within collections of jurisdictions. A stable partition of individuals is shown to exist for all sufficiently large economies. This stability depends, partially, upon the extent of ‘satisficing’ behavior or alternatively, jurisdiction formation costs, both of which can be made arbitrarily small. The major noteworthy assumption is that positive outputs cannot become virtually free in per-capita terms as the economy is replicated; this ensures that the public goods are ‘local’ rather than ‘pure’; otherwise assumptions on production sets are minimal and, in particular, convexity is not required. To obtain stability with coalition formation costs, additional assumptions are made ensuring that there is a ‘minimum efficient scale’ for coalitions.     

Incremental Operator Assistance Knowledge System—an intelligent aid for a general class of problems

A new approach for knowledge representation and inference is introduced and discussed in this paper which is applicable to a wide range of daily problems—practically for all the problems, where some ‘strategy’ for fault search and rectification is provided by an expert. The system is efficient even if this ‘strategy’—that is, the general understanding of the actual problem—is weak. The theory finds its application in the ADAC project, corresponding to a problem raised by Circuit Foil, Luxembourg, a leader in the copper foil industry.     

Allfinanz,bancassurance and the future of banking

The purpose with this paper is first to analyse the strategies of Allfinanz (Bancassurance) in Germany and then to investigate if the German banks have become more efficient during the period since Allfinanz was introduced. Two methods are used to analyse efficiency: ‘financial ratio analysis’ (FRA) and ‘data envelopment analysis’ (DEA). FRA is useful in studying the change in productivity. DEA generates, efficiency scores and alternative and more efficient combinations of banks.     

Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the developed class of bivariate counting processes are not regular. Therefore, the proposed class of processes allows simultaneous occurrences of two types of events, which can be applicable in practical modeling of counting events. Initially, some basic properties of the new class of bivariate counting processes will be discussed. Based on the obtained properties, the joint distributions of the numbers of events in time intervals will be derived and the dependence structure of the bivariate process will be discussed. Furthermore, the marginal and conditional processes will be studied. The application of the proposed bivariate counting process to a shock model will also be considered. In addition, the generalization to the multivariate counting processes will be discussed briefly.     

P-varieties - a signature independent characterization of varieties of ordered algebras

This paper is concerned mainly with classes (categories) of ordered algebras which in some signature are axiomatizable by a set of inequations between terms (‘varieties’ of ordered algebras) and also classes which are axiomatizable by implications between inequations (‘quasi varieties’ of ordered algebras). For example, if the signature contains a binary operation symbol (for the monoid operation) and a constant symbol (for the identity) the class of ordered monoids M can be axiomatized by a set of inequations (i.e. expressions of the form t≤t'. However, if the signature contains only the binary operation symbol, the same class M cannot be so axiomatized (since it is not now closed under subalgebras). Thus, there is a need to find structural, signature independent conditions on a class of ordered algebras which are necessary and sufficient to guarantee the existence of a signature in which the class is axiomatizable by a set of inequations (between terms in this signature). In this paper such conditions are found by utilizing the notion of ‘P-categories’. A P-category C is a category such that each ‘Hom-set’ C(a,b) is equipped with a distiguished partial order which is preserved by composition. Aside from proving the characterization theorem, it is also the purpose of the paper to begin the investigation of P-categories.     

Demographic transition and social security policies in France: A welfare analysis

A dynamic computable general equilibrium model with overlapping generations is used to appraise the consequences in France of three social security policies: a 20% cut in the replacement rate (‘TM20’), an increase in retirement age from 60 to 65 (‘RET65’), and the creation of a transitory fund (‘FUND’). These policies are described in three scenarios built up around a baseline scenario, in which the current French public pension system, financed on a pay-as-you-go basis, is maintained. Whatever the scenario, the demographic transition is assumed to be close to that described in official projections, in which the most likely fertility rate between years 1995 and 2050 is supposed to be equal to 1.8 children per woman. The main results are the following: maintaining the current system remains a reasonable option since slump should not occur during the transition period. Nevertheless, this option may seem undesirable because of the demographic risk—the realization of a scenario less favourable than the official one cannot be ruled out—and the lack of equity of the current pensions system. If equity is appraised with respect to a simple actuarial criterion (i.e. the ratio of the present value of pensions received by a generation over the present value of its social contributions), the ‘FUND’ option appears to be the most equitable. The ‘RET65’ option is the least fair since people presently working are worse off. When macroeconomic outcomes (e.g. per capita production or consumption) or social welfare are considered, the scenario in which the legal retirement age is increased seems to dominate all other options, owing to its huge effects. Nevertheless, these results hold under restrictive assumptions, among which the most crucial is full employment being restored quickly. The ‘FUND’ option is the less desirable, owing to ambiguous and small macroeconomic and social welfare effects. Finally, a 20% cut in the replacement rate would have intermediate effects: less additional production or welfare than in the ‘RET65’ scenario, but more than in ‘FUND’; less efficient in struggling against the lack of equity than the latter scenario, but more than the former.     

A risky asset model based on Lévy processes and asymptotically self-similar activity time processes with long-range dependence

In the paper,using Lvy processes subordinated by‘asymptotically self-similar activity time’processes with long-range dependence,we set up new asset pricing models.Using the diferent construction for gamma(Γ)based‘asymptotically self-similar activity time’processes with long-range dependence from Finlay and Seneta(2006)we extend the constructions for inverse-gamma and gamma based‘asymptotically selfsimilar activity time’processes with integer-valued parameters and long-range dependence in Heyde and Leonenko(2005)and Finlay and Seneta(2006)to noninteger-valued parameters.     

A stylized model of ‘Momentum’ processes: a research note

Several phenomena of interest like stock price movements, online auction bidprices or inventory levels, can be stylized as ‘momentum processes’,whereby the very start of activity (‘up’ or ‘down’) cantrigger subsequent activity in that direction. We calculate the transientprobabilities of being in a particular state (eg, stock price or current auctionbid level) in such activities. The calculations can be used to estimate theexpected time to reach a certain price, inventory level or bid. The processescan be modified to show the phenomenon where the lack of activity can have an‘inertia of rest’.     

Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited

The stability analysis introduced by Lyapunov and extended by Oseledec provides an excellent tool to describe the character of nonlinear n-dimensional flows by n global exponents if these flows are stationary in time. However, here we discuss two shortcomings: (a) the local exponents fail to indicate the origin of instability where trajectories start to diverge. Instead, their time evolution contains a much stronger chaos than the trajectories, which is only eliminated by integrating over a long time. Therefore, shorter time intervals cannot be characterized correctly, which would be essential to analyse changes of chaotic character as in transients. (b) Although Oseledec uses an n dimensional sphere around a point x to be transformed into an n dimensional ellipse in first order, this local ellipse has not yet been evaluated. The aim of this contribution is to eliminate these two shortcomings. Problem (a) disappears if the Oseledec method is replaced by a frame with a ‘constraint’ as performed by Rateitschak and Klages (RK) [Rateitschak K, Klages R, Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering. Phys Rev E 2002;65:036209/1–11]. The reasons why this method is better will be illustrated by comparing different systems. In order to analyze shorter time intervals, integrals between consecutive Poincaré points will be evaluated. The local problem (b) will be solved analytically by introducing the ‘symmetric Jacobian for local Lyapunov exponents’ and its orthogonal submatrix, which enable to search in the full phase space for extreme local separation exponents. These are close to the RK exponents but need no time integration of the RK frame. Finally, four sets of local exponents are compared: Oseledec frame, RK frame, symmetric Jacobian for local Lyapunov exponents and its orthogonal submatrix.     

A logical characterization of the Euclidean plane,sphere and cylinder

Within a mathemtaical theory, a structured set is called homogeneous,if its ‘parts’ cannot be distinguished from each other by statements of that theory. In Euclidean space geometry, among all convex surfaces and among all complete connected orientable 2‐manifolds with at least one regular point, there are only three types of homogeneous objects: the Euclidean plane, sphere and cylinder.     

Time-inhomogeneous discrete stochastic search methods for optimal Bernoulli parameters

We present two time-inhomogeneous search processes for finding the optimal Bernoulli parameters, where the performance measure cannot be evaluated exactly but must be estimated through Monte Carlo simulation. At each iteration, two neighbouring alternatives are compared and the one that appears to be better is passed on to the next iteration. The first search process uses an increasing sample size of each configuration at each iteration. The second search process uses a sequential sampling procedure with increasing boundaries as the number of iterations increases. At each iteration the acceptance of a new configuration depends on the iterate number, therefore, the search process turns out to be inhomogeneous Markov chain. We show that if the increase occurs slower than a certain rate, these search processes will converge to the optimal set with probability one. © 1998 John Wiley & Sons, Ltd.     

Do Material Things Have Intrinsic Properties?

Possession of any actual physical property depends on the ambient conditions for its bearers, irrespective of one's particular theory of dispositions. If ‘self-sufficiency’ makes a property intrinsic, then, because of this dependence, things in the actual world cannot have an intrinsic physical resemblance to one another or to things in other possible worlds. Criteria for the self-sufficiency of intrinsic properties based on, or implying indifference to both ‘loneliness’ and ‘accompaniment’ entail that no self-sufficient property can require its bearers to be extended in space or time, yet all physical properties of concrete objects do require this. These outcomes undermine the vindication of physicalism claimed by neo-Humeans for their metaphysical project. For physical properties dependent on ambient conditions cannot supervene on intrinsic properties independent of ambient conditions: when ambient conditions change we get a change in the former without a change in the latter.     

Uncertainty principles on certain Lie groups

There are several ways of formulating the uncertainty principle for the Fourier transform on ? ⁿ . Roughly speaking, the uncertainty principle says that if a functionf is ‘concentrated’ then its Fourier transform $\tilde f$ cannot be ‘concentrated’ unlessf is identically zero. Of course, in the above, we should be precise about what we mean by ‘concentration’. There are several ways of measuring ‘concentration’ and depending on the definition we get a host of uncertainty principles. As several authors have shown, some of these uncertainty principles seem to be a general feature of harmonic analysis on connected locally compact groups. In this paper, we show how various uncertainty principles take form in the case of some locally compact groups including ? ⁿ , the Heisenberg group, the reduced Heisenberg groups and the Euclidean motion group of the plane.     

Symmetry in de Branges almost Pontryagin spaces

In many examples of de Branges spaces symmetry appears naturally. Presence of symmetry gives rise to a decomposition of the space into two parts, the ‘even’ and the ‘odd’ part, which themselves can be regarded as de Branges spaces. The converse question is to decide whether a given space is the ‘even’ part or the ‘odd’ part of some symmetric space, and, if yes, to describe the totality of all such symmetric spaces. We consider this question in an indefinite (almost Pontryagin space) setting, and give a complete answer. Interestingly, it turns out that the answers for the ‘even’ and ‘odd’ cases read quite differently; the latter is significantly more complex.     

Myopia,amnesia, and consistent intertemporal choice

Social scientists often explain observed streams of behavior as the outcome of constrained choice at successive dates, with actors choosing among planned sequences of actions extending into the future. This paper presents four axioms for consistent intertemporal choice in such models. Within this framework, myopia and amnesia are defined to be choice processes in which future feasible actions and past decisions, respectively, play no role in current choice. Each of these modeling strategies is argued to have some plausibility on the basis of bounded rationality considerations. It is shown that an anticipatory process reduces to a behaviorally equivalent myopic process if and only if binary choices are lexically organized. Amnesia, or the absence of endogenous preference formation, is characterized by the condition that binary choices be ‘ahistorical’. The paper closes with some remarks on the methodological role of the consistency axioms, and the problems posed by inconsistent choice processes.     

Joint Determination of Production Cycle and Inspection Intervals in a Deteriorating Production System

This paper considers production-maintenance policy for the deteriorating production system which can go ‘out of control’ while producing items. Once out of control, the production process produces some proportion of defective items. The defective items are reworked at some cost before being shipped, or, if passed to the customer, incur much larger warranty cost. Thus, to operate this system economically, periodic inspection and restoration of the process are needed. A mathematical model representing the expected annual cost is developed to determine the production cycle and process inspection intervals jointly. A case of equally spaced inspection intervals is solved by using an approximation to the cost function.     

Hamilton cycles in plane triangulations

We extend Whitney's Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely, we define a decomposition of a plane triangulation G into 4‐connected ‘pieces,’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian. We provide an example to show that our hypothesis that each piece shares a triangle with at most three other pieces' cannot be weakened to ‘four other pieces.’ As part of our proof, we also obtain new results on Tutte cycles through specified vertices in planar graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 138–150, 2002