Perturbed Copula: Introducing the skew effect in the co-dependence

Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of this copula is derived through an asymptotic expansion under the assumption of a common fast mean reverting stochastic volatility factor. This paper applies this new perturbed copula to the valuation of derivative products; in particular FX quanto options to a third currency. A calibration procedure to fit the skew of both underlying securities is presented. The action of the perturbed copula is interpreted compared to the Gaussian copula. A real worked example is carried out comparing both copulas and a local volatility model with constant correlation for varying maturities, correlations and skew configurations.Comment: 34 pages, 6 figures and 3 table

Managed Trade, Trade Liberalisation and Local Pollution

The current paper addresses the relationship between trade and endogenous pollution levels. The main focus is quite different from the previous literature. The mechanism linking pollution and trade is that trade provides the home government with a credible threat that helps motivate domestic firms to adopt cleaner technologies. This credible threat comes from the fact that the government has a greater incentive to protect a clean industry than to protect a very polluting one. In that sense, the existence of trade helps reduce domestic pollution compared to what would prevail in a situation of autarky. On the other hand, a commitment to free trade would be counterproductive: it limits the government's ability to credibly threaten its domestic firms. In fact we show that any trade liberalisation hurts the welfare of the home country. In terms of world welfare, moderate trade liberalisation is helpful but only as long as it does no affect the technology choices of the firms.

A compact topology for sand automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable

Lateral fligh control design for a highly flexible aircraft using a nonsmooth method

This paper describes a nonsmooth optimization technique for designing a lateral flight control law for a highly flexible aircraft. Flexible modes and high-dimensional models pose a major challenge to modern control design tools. We show that the nonsmooth approach offers potent and flexible alternatives in this difficult context. More specifically, the proposed technique is used to achieve a mix of frequency domain as well as time domain requirements for a set of different flight conditions

Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Delta(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.Comment: 4 pages, 6 figure

Rare events statistics of random walks on networks: localization and other dynamical phase transitions

Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics can be studied in terms of spectral properties of a deformed Markov transition matrix. We observe two different types of phase transition in such systems: (i) rare events which are singled out for sufficiently large values of the deformation parameter may correspond to {\em localized\/} modes of the deformed transition matrix, (ii) "mode-switching transitions" may occur as the deformation parameter is varied. Details depend on the nature of the observable for which the rare event statistics is studied, as well as on the underlying graph ensemble. In the present letter we report on the statistics of the average degree of the nodes visited along a random walk trajectory in Erd\H{o}s-R\'enyi networks. Large deviations rate functions and localization properties are studied numerically. For observables of the type considered here, we also derive an analytical approximation for the Legendre transform of the large-deviations rate function, which is valid in the large connectivity limit. It is found to agree well with simulations.Comment: 5 pages, 3 figure

Perks as Second Best Optimal Compensations

The finance literature views perks either as productivity enhancing expenditures or as a result of poor managerial control by shareholders. Using a corporate jet to attend a business meeting may be justified because of the returns generated for the firm; but flying on the same jet to reach a vacation resort reflects a misappropriation of the firm’s resources by the manager. Our paper challenges this view. We argue that complementarity between leisure and wages creates difficult incentive problems, because the bonuses or stock options that reward success increase the marginal disutility of effort. In such a context, we show that whenever there exist commodities (‘perks’) that are substitute to leisure (or even less complementary to leisure than money), the optimal incentive scheme involves overprovision of such commodities, in the sense that the agent should consume more of them that she would elect to, should she be given a choice between money and perks at the current market prices. This conclusion is valid even when perks must be provided independently of the manager’s performace. Finally, we discuss the role of governance by introducing manipulations a la Peng and Röell (2006), and show that, in contrast with standard intuition, perks are used even when governance is perfect, and poorer governance may result in less perks being offered to the agent.Perks, Moral Hazard, Incentives, Second Best

The universal high temperature regime of pinned elastic objects

We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $\delta$-correlated disorder and that they are universal up to only two parameters that can be explicitly computed. This is shown numerically on the roughness of directed polymer models and by dimensional and functional renormalization group arguments. We discuss experimental consequences such as non-monotonous behaviour with temperature.Comment: 4 pages, 3 figure