The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

Differential effects of two virtual reality interventions: distraction versus pain control

There is evidence that virtual reality (VR) pain distraction is effective at improving pain-related outcomes. However, more research is needed to investigate VR environments with other pain-related goals. The main aim of this study was to compare the differential effects of two VR environments on a set of pain-related and cognitive variables during a cold pressor experiment. One of these environments aimed to distract attention away from pain (VRD), whereas the other was designed to enhance pain control (VRC). Participants were 77 psychology students, who were randomly assigned to one of the following three conditions during the cold pressor experiment: (a) VRD, (b) VRC, or (c) Non-VR (control condition). Data were collected regarding both pain-related variables (intensity, tolerance, threshold, time perception, and pain sensitivity range) and cognitive variables (self-efficacy and catastrophizing). Results showed that in comparison with the control condition, the VRC intervention significantly increased pain tolerance, the pain sensitivity range, and the degree of time underestimation. It also increased self-efficacy in tolerating pain and led to a reduction in reported helplessness. The VRD intervention significantly increased the pain threshold and pain tolerance in comparison with the control condition, but it did not affect any of the cognitive variables. Overall, the intervention designed to enhance control seems to have a greater effect on the cognitive variables assessed. Although these results need to be replicated in further studies, the findings suggest that the VRC intervention has considerable potential in terms of increasing self-efficacy and modifying the negative thoughts that commonly accompany pain problems.

Periodic solutions of second-order differential inclusions systems with p-Laplacian

Some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Periodic solutions for nonautonomous second order differential inclusions systems with p- Laplacian

Using the nonsmooth variant of minimax point theorems, some existence results are obtained for periodic solutions of nonautonomous second-order differential inclusions systems with p-Laplacian.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Limit Cycles for a class of three dimensional polynomial differential systems

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Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Polynomial and linearized normal forms for almost periodic differential systems

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Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities

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Business Cycle Regimes in CEECs Production: A Threshold SURE Approach

We use a threshold seemingly unrelated regressions specification to assess whether the Central and East European countries (CEECs) are synchronized in their business cycles to the Euro-area. This specification is useful in two ways: First, it takes into account the common institutional factors and the similarities across CEECs in their process of economic transition. Second, it captures business cycle asymmetries by allowing for the presence of two distinct regimes for the CEECs. As the CEECs are strongly affected by the Euro-area these regimes may be associated with Euro-area expansions and contractions. We discuss representation, estimation by maximum likelihood and inference. The methodology is illustrated by using monthly industrial production in 8 CEECs. The results show that apart from Lithuania the rest of the CEECs experience “normal” growth when the Euro-area contracts and “high” growth when the Euro-area expands. Given that the CEECs are “catching up” with the Euro-area this result shows that most CEECs seem synchronized to the Euro-area cycle. Keywords: Threshold SURE; asymmetry; business cycles; CEECs. JEL classification: C33; C50; E32.