Pricing of reinsurance contracts in the presence of catastrophe bonds

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process. Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered. The methodology is illustrated on several examples including Pareto and Gamma claim severities

Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission

A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy statistics of soft X-ray solar flares for class M and C is well described by a FARIMA time series with Pareto innovations. The model is characterized by two effects. One of them is a long-range dependence (long-term memory), and another corresponds to heavy-tailed distributions. Their parameters are statistically stable enough during the periods. However, when the solar activity tends to minimum, they change essentially. We discuss possible causes of this evolution and suggest a statistical model for predicting the flare energy statistics.Comment: 21 pages, 7 figure

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm

Single-molecule imaging reveals receptor-G protein interactions at cell surface hot spots

G-protein-coupled receptors mediate the biological effects of many hormones and neurotransmitters and are important pharmacological targets. They transmit their signals to the cell interior by interacting with G proteins. However, it is unclear how receptors and G proteins meet, interact and couple. Here we analyse the concerted motion of G-protein-coupled receptors and G proteins on the plasma membrane and provide a quantitative model that reveals the key factors that underlie the high spatiotemporal complexity of their interactions. Using two-colour, single-molecule imaging we visualize interactions between individual receptors and G proteins at the surface of living cells. Under basal conditions, receptors and G proteins form activity-dependent complexes that last for around one second. Agonists specifically regulate the kinetics of receptor-G protein interactions, mainly by increasing their association rate. We find hot spots on the plasma membrane, at least partially defined by the cytoskeleton and clathrin-coated pits, in which receptors and G proteins are confined and preferentially couple. Imaging with the nanobody Nb37 suggests that signalling by G-protein-coupled receptors occurs preferentially at these hot spots. These findings shed new light on the dynamic interactions that control G-protein-coupled receptor signalling

Modelling catastrophe claims with left-truncated severity distributions

Natural catastrophe, Property insurance, Loss distribution, Truncated data, Ruin probability,