Excess of loss reinsurance under joint survival optimality

Explicit expressions for the probability of joint survival up to time x of the cedent and the reinsurer, under an excess of loss reinsurance contract with a limiting and a retention level are obtained, under the reasonably general assumptions of any non-decreasing premium income function, Poisson claim arrivals and continuous claim amounts, modelled by any joint distribution. By stating appropriate optimality problems, we show that these results can be used to set the limiting and the retention levels in an optimal way with respect to the probability of joint survival. Alternatively, for fixed retention and limiting levels, the results yield an optimal split of the total premium income between the two parties in the excess of loss contract. This methodology is illustrated numerically on several examples of independent and dependent claim severities. The latter are modelled by a copula function. The effect of varying its dependence parameter and the marginals, on the solutions of the optimality problems and the joint survival probability, has also been explored

Ruin and Deficit Under Claim Arrivals with the Order Statistics Property

We consider an insurance risk model with extended flexibility, under which claims arrive according to a point process with an order statistics (OS) property, their amounts may have any joint distri- bution and the premium income is accumulated following any non- decreasing, possibly discontinuous real valued function. We generalize the definition of an OS point process, assuming it is generated by an arbitrary cdf allowing jump discontinuities, which corresponds to an arbitrary (possibly discontinuous) claim arrival cumulative intensity function. The latter feature is appealing for insurance applications since it allows to consider clusters of claims arriving instantaneously. Under these general assumptions, a closed form expression for the joint distribution of the time to ruin and the deficit at ruin is derived, which remarkably involves classical Appell polynomials. Corollaries of our main result generalize previous non-ruin formulas e.g., those obtained by Ignatov and Kaishev (2000, 2004, 2006) and Lef`evre and Loisel (2009) for the case of stationary Poisson claim arrivals and by Lef`evre and Picard (2011, 2014), for OS claim arrivals

Operational risk and insurance: a ruin probabilistic reserving approach

A new methodology for financial and insurance operational risk capital estimation is proposed. It is based on using the finite time probability of (non-)ruin as an operational risk measure, within a general risk model. It allows for inhomogeneous operational loss frequency (dependent inter-arrival times) and dependent loss severities which may have any joint discrete or continuous distribution. Under the proposed methodology, operational risk capital assessment is viewed not as a one off exercise, performed at some moment of time, but as dynamic reserving, following a certain risk capital accumulation function. The latter describes the accumulation of risk capital with time and may be any nondecreasing, mpositive real function hHtL. Under these reasonably general assumptions, the probability of mnon-ruin is explicitly expressed using closed form expressions, derived by Ignatov and Kaishev (2000, 2004, 2007) and Ignatov, Kaishev and Krachunov (2001) and by setting it to a high enough preassigned mvalue, say 0.99, it is possible to obtain not just a value for the capital charge but a (dynamic) risk capital accumulation strategy, hHtL. In view of its generality, the proposed methodology is capable of accommodating any (heavy tailed) mdistributions, such as the Generalized Pareto Distribution, the Lognormal distribution the g-and-h mdistribution and the GB2 distribution. Applying this methodology on numerical examples, we demonstrate that dependence in the loss severities may have a dramatic effect on the estimated risk capital. In addition, we show also that one and the same high enough survival probability may be achieved by mdifferent risk capital accumulation strategies one of which may possibly be preferable to accumulating capital just linearly, as has been assumed by Embrechts et al. (2004). The proposed methodology takes into account also the effect of insurance on operational losses, in which case it is proposed to take the probability of joint survival of the financial institution and the insurance provider as a joint operational risk measure. The risk capital allocation strategy is then obtained in such a way that the probability of joint survival is equal to a preassigned high enough value, say 99.9

Ruin and deficit at ruin under an extended order statistics risk process

We consider an insurance risk model with extended flexibility, under which claims arrive according to a point process with an order statistics (OS) property, their amounts may have any joint distribution and the premium income is accumulated following any nondecreasing, possibly discontinuous real valued function. We generalize the definition of an OS point process, assuming it is generated by an arbitrary cdf, allowing jump discontinuities which corresponds to an arbitrary (possibly discontinuous) claim arrival cumulative intensity function. The latter feature is appealing for insurance applications since it allows to consider clusters of claims arriving instantaneously. Under these general assumptions, a closed form expression for the joint distribution of the time to ruin and the deficit at ruin is derived, which remarkably involves classical Appell polynomials. Corollaries of our main result generalize previous non-ruin formulas e.g., those obtained by Ignatov and Kaishev (2000, 2004, 2006) and Lef`evre and Loisel (2009) for the case of stationary Poisson claim arrivals and by Lef`evre and Picard (2011, 2014), for OS claim arrivals

Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field

We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.Comment: 8 pages, Revtex, 3 Postscript figure

Optimal joint survival reinsurance: An efficient frontier approach

The problem of optimal excess of loss reinsurance with a limiting and a retention level is considered. It is demonstrated that this problem can be solved, combining specific risk and performance measures, under some relatively general assumptions for the risk model, under which the premium income is modelled by any non-negative, non-decreasing function, claim arrivals follow a Poisson process and claim amounts are modelled by any continuous joint distribution. As a performance measure, we define the expected profits at time x of the direct insurer and the reinsurer, given their joint survival up to x, and derive explicit expressions for their numerical evaluation. The probability of joint survival of the direct insurer and the reinsurer up to the finite time horizon x is employed as a risk measure. An efficient frontier type approach to setting the limiting and the retention levels, based on the probability of joint survival considered as a risk measure and on the expected profit given joint survival, considered as a performance measure is introduced. Several optimality problems are defined and their solutions are illustrated numerically on several examples of appropriate claim amount distributions, both for the case of dependent and independent claim severitie

Nonlinear dynamics of large amplitude dust acoustic shocks and solitary pulses in dusty plasmas

We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves. Time-dependent numerical solutions of our nonlinear model compare favorably well with the recent experimental works (mentioned above) that have reported the formation of large amplitude non-stationary DA shocks and DA solitary pulses in low-temperature dusty plasma discharges.Comment: 9 pages, 4 figures. To be published in Physical Review

Suppressed absolute negative conductance and generation of high-frequency radiation in semiconductor superlattices

We show that space-charge instabilities (electric field domains) in semiconductor superlattices are the attribute of absolute negative conductance induced by small constant and large alternating electric fields. We propose the efficient method for suppression of this destructive phenomenon in order to obtain a generation at microwave and THz frequencies in devices operating at room temperature. We theoretically proved that an unbiased superlattice with a moderate doping subjected to a microwave pump field provides a strong gain at third, fifth, seventh, etc. harmonics of the pump frequency in the conditions of suppressed domains.Comment: 8 pages. Development of cond-mat/0503216 . Version 2: Final version, erratum is include

Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach

Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For the Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasma in the framework of the PT approach. The relation between this force, negative collecting friction force and scattering and collecting drag forces is established.+AFwAXA- The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.+AFwAXA- PACS number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page

Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices

We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model, and the properties of the solutions are analyzed. An expression for the current is obtained. Finally, Zener-tunneling in a two-band tight-binding model is considered. The present work gives the background and an extension of the theoretical framework underlying our recent Letter [J. Rotvig {\it et al.}, Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache