Semi-groups and time operators for quantum unstable systems

We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states characterized in terms of the Hardy class

Space-time directional Lyapunov exponents for cellular automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved

Directional complexity and entropy for lift mappings

We introduce and study the notion of a directional complexity and entropy for maps of degree 1 on the circle. For piecewise affine Markov maps we use symbolic dynamics to relate this complexity to the symbolic complexity. We apply a combinatorial machinery to obtain exact formulas for the directional entropy, to find the maximal directional entropy, and to show that it equals the topological entropy of the map. Keywords: Rotation interval, Space-time window, Directional complexity, Directional entropy;Comment: 19p. 3 fig, Discrete and Continuous Dynamical Systems-B (Vol. 20, No. 10) December 201

Longevity risks and capital markets: The 2010-2011 update

This Special Issue of Geneva Papers on Risk and Insurance - Issues and Practice contains 10 contributions to the academic literature all dealing with longevity risk and capital markets. Draft versions of the papers were presented at Longevity Six: The Sixth International Longevity Risk and Capital Markets Solutions Conference that was held in Sydney on 9-10 September 2010. It was hosted by the Australian Institute for Population Ageing Research, the Australian School of Business and the University of New South Wales. It was sponsored by PricewaterhouseCoopers, Australian Prudential Regulation Authority (APRA), Coventry Capital, Swiss Re, and Institute of Actuaries of Australia.Longevity Risk; Capital Market

Primes de risque et soins de santé

Dans ce travail, nous appliquons la notion de prime de risque à une situation pour laquelle l’individu est confronté à un risque de maladie qui peut engendrer un risque de richesse via le recours aux soins de santé. Suivant la nature des soins entrepris, différentes primes sont définies qui vérifient pour la plupart les propriétés usuelles des primes à la Arrow-Pratt. Enfin, la comparaison de ces primes nous renseigne sur les préférences individuelles en matière de soins de santé.In this work, the notion of risk premium is applied to a situation for which the individual is confronted with a risk of illness. This health risk can breed a risk of wealth via the recourse to health care. Following the nature of health care undertaken, different premiums are defined which verify the usual properties of the Arrow-Pratt risk premiums. Finally, the comparison of these premiums informs us of the individual preferences in terms of health care

On Bivariate Risk Premia

This note examines the conditions under which the bivariate risk premium for one risk may be negative even if both risks are positively correlated, using a mean variance setting. The link between the bivariate risk premium and the partial bivariate risk premia is also investigate

Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO