Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

A computable general equilibrium analysis of the relative price sensitivity required to induce rebound effects in response to an improvement in energy efficiency in the UK economy

In recent years there has been extensive debate in the energy economics and policy literature on the likely impacts of improvements in energy efficiency. This debate has focussed on the notion of rebound effects. Rebound effects occur when improvements in energy efficiency actually stimulate the direct and indirect demand for energy in production and/or consumption. This phenomenon occurs through the impact of the increased efficiency on the effective, or implicit, price of energy. If demand is stimulated in this way, the anticipated reduction in energy use, and the consequent environmental benefits, will be partially or possibly even more than wholly (in the case of ‘backfire’ effects) offset. A recent report published by the UK House of Lords identifies rebound effects as a plausible explanation as to why recent improvements in energy efficiency in the UK have not translated to reductions in energy demand at the macroeconomic level, but calls for empirical investigation of the factors that govern the extent of such effects. Undoubtedly the single most important conclusion of recent analysis in the UK, led by the UK Energy Research Centre (UKERC) is that the extent of rebound and backfire effects is always and everywhere an empirical issue. It is simply not possible to determine the degree of rebound and backfire from theoretical considerations alone, notwithstanding the claims of some contributors to the debate. In particular, theoretical analysis cannot rule out backfire. Nor, strictly, can theoretical considerations alone rule out the other limiting case, of zero rebound, that a narrow engineering approach would imply. In this paper we use a computable general equilibrium (CGE) framework to investigate the conditions under which rebound effects may occur in the Scottish regional and UK national economies. Previous work has suggested that rebound effects will occur even where key elasticities of substitution in production are set close to zero. Here, we carry out a systematic sensitivity analysis, where we gradually introduce relative price sensitivity into the system, focusing in particular on elasticities of substitution in production and trade parameters, in order to determine conditions under which rebound effects become a likely outcome. We find that, while there is positive pressure for rebound effects even where (direct and indirect) demand for energy is very price inelastic, this may be partially or wholly offset by negative income and disinvestment effects, which also occur in response to falling energy prices.

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985).

Information Design

There are two ways of creating incentives for interacting agents to behave in a desired way. One is by providing appropriate payoff incentives, which is the subject of mechanism design. The other is by choosing the information that agents observe, which we refer to as information design. We consider a model of symmetric information where a designer chooses and announces the information structure about a payoff relevant state. The interacting agents observe the signal realizations and take actions which affect the welfare of both the designer and the agents. We characterize the general finite approach to deriving the optimal information structure for the designer - the one that maximizes the designer's ex ante expected utility subject to agents playing a Bayes Nash equilibrium. We then apply the general approach to a symmetric two state, two agent, and two actions environment in a parameterized underlying game and fully characterize the optimal information structure: it is never strictly optimal for the designer to use conditionally independent private signals; the optimal information structure may be a public signal or may consist of correlated private signals. Finally, we examine how changes in the underlying game affect the designer's maximum payoff. This exercise provides a joint mechanism/information design perspective.

Modeling Dependence Structure and Forecasting Market Risk with Dynamic Asymmetric Copula

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct “high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate its usefulness by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for the high-minus-low portfolios. From back-testing, e find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.