Practical approximations for multivariate characteristics of risk processes

The author gratefully acknowledges the financia support from: Bacas de Perfeccionamiento de Doctores en el Extranjero, 1999, MEC, SpainPublicad

Calculating multivariate ruin probabilities via Gaver–Stehfest inversion technique

Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the Gaver–Stehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literaturePublicad

Finite time ruin probabilities with one Laplace inversion

In this work we present an explicit formula for the Laplace transform in time of the finite time ruin probabilities of a classical Levy model with phase-type claims. Our result generalizes the ultimate ruin probability formula of Asmussen and Rolski [IME 10 (1991) 259]—see also the analog queuing formula for the stationary waiting time of the M/Ph/1 queue in Neuts [Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore, MD, 1981]—and it considers the deficit at ruin as wellPublicad

The Gerber-Shiu expected discounted penalty-reward function under an affine jump-diffusion model

We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004)Publicad

A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process

A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at a constant rate with additional random fluctuation. The insurer is allowed to invest the surplus into a risky asset with volatility dependent on the level of the investment, which permits the incorporation of rational investment strategies as proposed by Berk and Green (2004). The return on investment is modulated by a Markov process which generalizes previously studied settings for the evolution of the interest rate in time. The Gerber–Shiu expected penalty–reward function is studied in this context, including ruin probabilities (a first-passage problem) as a special case. The second order integro-differential system of equations that characterizes the function of interest is obtained. As a closed-form solution does not exist, a numerical procedure based on the Chebyshev polynomial approximation through a collocation method is proposed. Finally, some examples illustrating the procedure are presentedPublicad

On the valuation ofconstant barrier options under spectrally one-sided exponential L&evy models and Carr’s approximation for American puts

This paper provides a general framework for pricing options with a constant barrier under spectrally one-sided exponential L&evy model, and uses it to implement ofCarr’s approximation for the value of the American put under this model. Simple analytic approximations for the exercise boundary and option value are obtained. c 2002 Elsevier Science B.V. All rights reservedPublicad

Apego y Psicosis. La importancia de la teoría vincular en la adherencia al tratamiento

La presente investigacion tiene como objetivo describir la posible relación existente entre los estilos de apego y la adherencia terapeútica en sujetos diagnosticados de esquizofrenia o psicosis. Para ello, se utilizo un diseño no experimental, de tipo descriptivo, transversal. La muestra quedo conformada por 20 sujetos adultos asistentes al Centro de Día Romareda o ingresados en regimen de Media Estancia en el C.R.P "Nuestra Señora del Pilar". Los instrumentos aplicados fueron: cuestionario de Apego Adulto de Melero y Cantero [1] y las Escalas de Adherencia al Servicio de enfermeía, al tratamiento psicoterapeútico y al centro diseñados para el estudio. Se encontró una mayor presencia de apego inseguro en la muestra frente al seguro. Los sujetos seguros presentaron mayores porcentajes de adherencia terapeútica frente a los sujetos con estilo inseguro; dentro de estos los sujetos preocupados presentaron a su vez mayor adherencia y los evitativos o alejados menor. Los resultados encontrados concuerdan con las hipotesis sugeridas por otros autores: mayor presencia de apego inseguro en pacientes psicoticos