Equilibria with nonstandard prices in vector lattice overlapping generations economies

The paper investigates overlapping generations (OLG) economies in vector lattices framework. Agents' preferences are assumed uniformly proper, though they may be nontransitive and incomplete. Existence is stated for the “equilibrium with nonstandard prices,” a notion that may be looked upon as a particular (or generalized, in other aspect) case of known “compensated equilibria” of OLG-economies. The difference is that compensated values are described via explicit formula given in nonstandard analysis terms. This approach enables more clear economic interpretation and shows some new properties of compensated values, such as their linearity over agents' endowments. Also it allows easy to prove the existence of equilibria under classical additional assumptions on agents' endowments.     

The secondary benefits of climate change mitigation: an overlapping generations approach

We modify a model of climate and economy to address the effects of the reduction in atmospheric pollutants which occurs as a result of climate change mitigation policies. In particular, the reduction of sulphur dioxide (SO₂) emissions as a result of climate change policies leads to reduced statistical morbidity and infant mortality, but increased short term climate change. It remains the case, even with the consideration of secondary benefits, that there are welfare costs of GHG emission control to almost all working-age agents alive when the policies are imposed, which suggests that the consideration of secondary benefits alone may not be sufficient to provoke aggressive action on climate change. Olivier Bahn—Affiliated researcher: GERAD, Bahn acknowledges the support of NSERC. Andrew Leach—Affiliated researcher: CABREE, CIRANO, CIRPEE.     

Optimal mix between pay-as-you-go and funding for DC pension schemes in an overlapping generations model

Public pension systems are usually pay-as-you-go financed, that is, current contributions cover the pension expenditures. However, some countries combine funding and pay-as-you-go within the first pillar. This article studies a mixed system where a part of the individual’s contribution accrues funded rights whereas the other part accrues pay-as-you-go rights. Diversification conditions between these two financing techniques are derived in a mean–variance framework for two distinct contexts: for a cohort entering the system (named ex-ante case) and for multiple cohorts coexisting at the same period of time (named ex-post case). The diversification benefits in presence of a liquidity constraint which ensures that the income from contributions is sufficient to cover the pension expenditures are also studied. We show that, on the one hand, diversification benefits individuals when the economy is dynamically efficient for the ex-ante case. On the other hand, diversification is unattractive when pay-as-ou-go and funding are positively correlated for the ex-post case.     

Controlling indeterminacy in Massey triple products

A technique is discussed to control the indeterminacy in cohomology Massey triple products. It involves finding cohomology classes with certain properties. Poincaré duality spaces always have such classes if the coefficients are in a field.     

Equivariant resolution of points of indeterminacy

We prove an equivariant form of Hironaka's theorem on elimination of points of indeterminacy. Our argument uses canonical resolution of singularities and an extended version of Sumihiro's equivariant Chow lemma.

     

Orthogonal polynomials for weights close to indeterminacy

We obtain estimates for Christoffel functions and orthogonal polynomials for even weights that are ‘close’ to indeterminate weights. Our main example is exp(-|x|(log|x|)^β), with β real, possibly modified near 0, but our results also apply to exp(-|x|^α(log|x|)^β),α<1. These types of weights exhibit interesting properties largely because they are either indeterminate or are close to the border between determinacy and indeterminacy in the classical moment problem.     

A reproducing kernel condition for indeterminacy in the multidimensional moment problem

Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen, and Ismail's 2002 result. We also present a class of measures for which the existence of a reproducing kernel implies indeterminacy.

     

Eliminating indeterminacy for localized solutions to reaction-diffusion equations in multidimensional domains

Exponentially ill-conditioned localized solutions are constructed asymptotically in the limit of small diffusion for two classes of singularly perturbed reaction-diffusion equations in a multidimensional domain.     

Tackling the Challenge of the Nineties

In this annual Blackett Lecture the experience of pursuing the challenge of rational planning and decision-making in London Transport is discussed. Secondly, some of the major challenges affecting all large business organizations in the 1990s are described. Thirdly, the characteristics which enable organizations to respond effectively to these challenges, and which help ensure their survival and success, are delineated.     

Sustainability,indeterminacy and oscillations in a growth model with environmental assets

We consider an economy where welfare of a continuum of (identical) agents depends on three goods: leisure, a free access renewable environmental asset and a produced good which can be consumed or saved to accumulate physical capital. We assume that aggregate consumption depletes the natural resource and that economic agents take as exogenously given the negative impact on the environmental asset by aggregate consumption. In this context, we show that indeterminacy and oscillating behavior may arise.     

Tackling the jump number of interval orders

Although the jump number problem for partially ordered sets in NP-complete in general, there are some special classes of posets for which polynomial time algorithms are known.Here we prove that for the class of interval orders the problem remains NP-complete. Moreover we describe another 3/2-approximation algrithm (two others have been developed already by Felsner and Syslo, respectively) by using a polynomial time subgraph packing algorithm.     

One-mode three-way overlapping cluster analysis

The present paper introduces an overlapping cluster analysis model and an associated algorithm that can analyze one-mode three-way similarities. The present model is an extension of ADCLUS model, and the present algorithm is based on the MAPCLUS algorithm. In the present model, one-mode three-way similarities are represented by the sum of the numerical weights of clusters to which any triplet of objects belongs. The present model and algorithm were applied to joint purchase data, and compared the result with that of MAPCLUS to show that the present model is effective in representing one-mode three-way similarities.     

More results on overlapping squares

Three recent papers (Fan et al., 2006; Simpson, 2007; Kopylova and Smyth, 2012) [5], [11], [8] have considered in complementary ways the combinatorial consequences of assuming that three squares overlap in a string. In this paper we provide a unifying framework for these results: we show that in 12 of 14 subcases that arise the postulated occurrence of three neighboring squares forces a breakdown into highly periodic behavior, thus essentially trivial and easily recognizable. In particular, we provide a proof of Subcase 4 for the first time, and we simplify and refine the previously established results for Subcases 11–14.     

A generalized Stieltjes criterion for the complete indeterminacy of interpolation problems

The main result of this paper is a generalized Stieltjes criterion for the complete indeterminacy of interpolation problems in the Stieltjes class. This criterion is a generalization to limit interpolation problems of the classical Stieltjes criterion for the indeterminacy of moment problems. It is stated in terms of the Stieltjes parameters M _j and N _j . We obtain explicit formulas for the Stieltjes parameters. General constructions are illustrated by examples of the Stieltjes moment problem and the Nevanlinna-Pick problem in the Stieltjes class.     

Enumerating cycles in the graph of overlapping permutations

The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length $n$ and edges that are permutations of length $n+1$ in which an edge $a_1?a_{n+1}$ would connect the standardization of $a_1?a_n$ to the standardization of $a_2?a_{n+1}$. We examine properties of this graph to determine where directed cycles can exist, to count the number of directed $2$-cycles within the graph, and to enumerate the vertices that are contained within closed walks and directed cycles of more general lengths.