Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems

We consider Hamiltonian systems near equilibrium that can be (formally) reduced to one degree of freedom. Spatio-temporal symmetries play a key role. The planar reduction is studied by equivariant singularity theory with distinguished parameters. The method is illustrated on the conservative spring-pendulum system near resonance, where it leads to integrable approximations of the iso-energetic Poincaré map. The novelty of our approach is that we obtain information on the whole dynamics, regarding the (quasi-) periodic solutions, the global configuration of their invariant manifolds, and bifurcations of these.

Invariant theory of abelian transvection groups

Let $G$ be a finite group acting linearly on the vector space $V$ over a field of arbitrary characteristic. The action is called {\em coregular} if the invariant ring is generated by algebraically independent homogeneous invariants and the {\em direct summand property} holds if there is a surjective $k[V]^G$-linear map $\pi:k[V]\to k[V]^G$. The following Chevalley--Shephard--Todd type theorem is proved. Suppose $G$ is abelian, then the action is coregular if and only if $G$ is generated by pseudo-reflections and the direct summand property holds.Comment: 9 page

The home bias of the poor: terms of trade effects and portfolios across the wealth distribution

Wealthier people generally hold a larger part of their savings in risky assets. Using the US Survey of Consumer Finances, I show that wealthier households also have a higher portfolio share of foreign assets. This relative home bias of the poor does not seem to be explained by fixed participation costs alone, as the portfolio share of foreign assets increases with financial wealth even among participants in foreign asset markets. This paper shows how both biases of poorer agents' portfolios, towards safe and home assets, can arise in a simple 2 country economy with income and portfolio heterogeneity. Poor investors are naturally biased against domestic equity when wages and capital returns are positively correlated, making equity a bad hedge against fluctuations in labour income relative to bonds. Moreover poor investors prefer home to foreign bonds if equilibrium terms of trade movements systematically lead to a fall in the purchasing power of domestic assets in periods of high wages. I show that this is likely to be the case if aggregate supply shocks at home are more important than abroad. Finally, the model shows that aggregate home bias in the country portfolio implies relative home bias of the poor and vice versa.Heterogeneous Agents, Home Bias, Inequality, International Asset Diversification, Portfolio Choice

Emerging Market Lending: Is Moral Hazard Endogenous?

This paper looks at the effect of moral hazard, resulting from information asymmetries in financial markets, on growth in financially open developing countries. We show that if domestic entrepreneurs can gamble with foreign creditors' money, borrowing under standard debt contracts is constrained by a No-Gambling Condition similar to that of Hellmann, Murdock, and Stiglitz (2000). However, this incentive constraint is endogenous in the development process: growth increases entrepreneurs' own capital at risk, thus reducing gambling incentives, but it decreases profitability of capital investment, which has the opposite effect. General equilibrium under moral hazard shows a unique and stable steady state, but involves at least temporary rationing of profitable projects and possibly capital flight from developing countries.

EMERGING MARKET LENDING: IS MORAL HAZARD ENDOGENOUS?

This paper shows how growth in financially open developing countries is affected when relations with international lenders suffer from the danger of moral hazard. We find that if entrepreneurs can gamble with foreign creditors¡¯ money, borrowing under standard debt contracts is constrained by a No-Gambling Condition similar to that in Hellmann, Murdock, and Stiglitz (2000). However, this incentive constraint is endogenous in the development process: growth increases entrepreneurs¡¯ own capital at risk and thus reduces incentives to gamble. But capital accumulation also decreases the profitability of investment, which has the opposite effect. General equilibrium under moral hazard shows a unique and stable steady state, but involves at least temporary rationing of profitable projects and possibly positive net investment by developing countries in international financial markets.Moral Hazard, Asymmetric Information, Open Economy Growth, International Finance

Hill's equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena

A simple example is considered of Hill's equation x" + (a^2 + bp(t))x = 0, where the forcing term p, instead of periodic, is quasi periodic with two frequencies. A geometric exploration is carried out of certain resonance tongues, containing instability pockets. This phenomenon in the perturbative case of small |b|, can be explained by averaging. Next a numerical exploration is given for the global case of arbitrary b, where some interesting phenomena occur. Regarding these, a detailed numerical investigation and tentative explanations are presented.

Enabling low-carbon living in new UK housing developments

Purpose: The purpose of this paper is to describe a tool (the Climate Challenge Tool) that allows house builders to calculate whole life carbon equivalent emissions and costs of various carbon and energy reduction options that can be incorporated into the design of new developments. Design/methodology/approach: The tool covers technical and soft (or lifestyle) measures for reducing carbon production and energy use. Energy used within the home, energy embodied in the building materials, and emissions generated through transport, food consumption and waste treatment are taken into account. The tool has been used to assess the potential and cost-effectiveness of various carbon reduction options for a proposed new housing development in Cambridgeshire. These are compared with carbon emissions from a typical UK household. Findings: The tool demonstrated that carbon emission reductions can be achieved at much lower costs through an approach which enables sustainable lifestyles than through an approach which focuses purely on reducing heat lost through the fabric of the building and from improving the heating and lighting systems. Practical implications: The tool will enable house builders to evaluate which are the most cost-effective measures that they can incorporate into the design of new developments in order to achieve the significant energy savings and reduction in carbon emissions necessary to meet UK Government targets and to avoid dangerous climate change. Originality/value: Current approaches to assessing carbon and energy reduction options for new housing developments concentrate on energy efficiency options such as reducing heat lost through the fabric of the building and improving the heating and lighting systems, alongside renewable energy systems. The Climate Challenge Tool expands the range of options that might be considered by developers to include those affecting lifestyle choices of future residents. © Emerald Group Publishing Limited

Modules of covariants in modular invariant theory

Let the finite group $G$ act linearly on the vector space $V$ over the field $k$ of arbitrary characteristic. If $H<G$ is a subgroup the extension of invariant rings $k[V]^G\subset k[V]^H$ is studied using modules of covariants. An example of our results is the following. Let $W$ be the subgroup of $G$ generated by the reflections in $G$. A classical theorem due to Serre says that if $k[V]$ is a free $k[V]^G$-module then $G=W$. We generalize this result as follows. If $k[V]^H$ is a free $k[V]^G$-module then $G$ is generated by $H$ and $W$, and the invariant ring $k[V]^{H\cap W}$ is free over $k[V]^W$ and generated as an algebra by $H$-invariants and $W$-invariants.Comment: 36 pages, proofs of main theorems have been improve