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 presentedExpected penalty–reward function; Markov-modulated process; Jump–diffusion process; Volterra integro-differential system of equations;

Risk theory and optimal control of Lévy driven processes

Esta tesis contiene tres artículos de investigación con aportes originales. El primer artículo, que coincide con el Capítulo 2, ha sido publicado (Diko and Usabel (17)) en Insurance: Mathematics and Economics, una revista de reconocimiento internacional incluída en JCR. En el citado capítulo se propone un método numérico que permite evaluar la función de utilidad en un marco de proceso de Poisson compuesto con cambio de régimen. Esto supone que los parámetros del modelo de Poisson compuesto pueden variar en el tiempo, gobernados por un proceso de Markov subyacente. Este modelo es una generalización de los procesos que se analizan en la literatura relevante hasta el momento, por tanto el aporte de este capítulo consiste tanto en el desarrollo de un modelo nuevo, capaz de reflejar un entorno económico variable, como en el método de cálculo de cuantías de interés relacionadas con este. Estas incluyen entre otras la probabilidad de la ruina, supervivencia o el déficit medio al producirse la ruina. El Capítulo 3 expone el tratamiento genérico de un problema de control estocástico en el marco de procesos generales de difusión de Lévy. Este tipo de problemas es conocido por su difficultad a la hora de obtener soluciones concretas, ya que las equaciones diferenciales o integro-diferenciales que caracterizan la solución no admiten tratamiento analítico exacto. Habitualmente se aplican métodos numéricos de discretización de tiempo. En esta tesis, se desarrolla un método de solución alternativo que consiste en Erlangizar (dividir en intervalos aleatorios exponenciales) el horizonte temporal establecido con lo que se consigue simplificar la complejidad de las equaciones diferenciales involucradas. Esta transformación lleva a una metodología de aproximación iterativa aplicable a un gran abanico de problemas del area de finanzas y seguros. Los resultados de este capíulo están en el proceso de revisión en Mathematical Finance, una de las revistas de finanzas estocásticas más importantes en el mundo. Por último, el Capíulo 4 ofrece una aplicación de la metodología presentada anteriormente en el marco de solvencia de una compañía de seguros. En este contexto se plantea un problema de decisión sobre la composición de la cartera de inversión optima con el fin de maximizar la utilidad esperada de una cartera sometida a un proceso de riesgo. Aplicando el algoritmo iterativo del Capítulo 3 se calculan las cuantías de interés y se demuestra la rápida convergencia y buenas propiedades del método propuesto. El contenido de este capítulo también representa un aporte original y está actualmente bajo revisión en la revista ASTIN Bulletin, referente principal en el campo de investigación actuarial. En conlusi on, los tres aportes de investigaci on original presentados en esta tesis permiten una aplicación de métodos numéricos para obtener resultados concretos en situaciones que hasta ahora no han sido tratadas en la literaturaChebyshev approximation in risk processes. Optimal control of Lévy diffusions. Risk theory and optimal investmen

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

A novel concept of short-flux path switched reluctance motor for electrical vehicles

This paper deals with the design of a novel Switched Reluctance Motor (SRM) with short flux path for electrical vehicles. Design consists of the segmented water cooled stator with the toroidal winding and the rotor with salient poles also in a form of segments. The SRM dimensions have been calculated on the base of input requirements. The static and dynamic parameters of SRM are obtained from simulation models based on Finite element method and torque, power versus speed characteristics are presented

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 presented.Expected penalty-reward function Markov-modulated process Jump-diffusion process Volterra integro-differential system of equations IM11 IM13

La morfometria analitica nella caratterizzazione dei meningiomi intracranici

Dottorato di ricerca in morfometria analitica ed applicazioni biomediche ed antropologiche. 7. ciclo. A.a. 1991-95. Coordinatore R. RiccoConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Proportions of CD4 test results indicating advanced HIV disease remain consistently high at primary health care facilities across four high HIV burden countries.

BACKGROUND:Globally, nearly 22 million HIV-infected patients are currently accessing antiretroviral treatment; however, almost one million people living with HIV died of AIDS-related illnesses in 2018. Advanced HIV disease remains a significant issue to curb HIV-related mortality. METHODS:We analyzed 864,389 CD4 testing records collected by 1,016 Alere Pima Analyzers implemented at a variety of facilities, including peripheral facilities, between January 2012 and December 2016 across four countries in sub-Saharan Africa. Routinely collected data and programmatic records were used to analyze the median CD4 counts and proportions of patients with advanced HIV disease by country, facility type, and year. RESULTS:Median CD4 counts were between 409-444 cells/ul each year since 2012 with a median in 2016 of 444 cells/ul (n = 319,829). The proportion of test results returning CD4 counts above 500 cells/ul has increased slowly each year with 41.8% (95% CI: 41.6-41.9%) of tests having a CD4 count above 500 cells/ul in 2016. Median CD4 counts were similar across facility types. The proportion of test results indicating advanced HIV disease has remained fairly consistent: 19.4% (95% CI: 18.8-20.1%) in 2012 compared to 16.1% (95% CI: 16.0-16.3%) in 2016. The proportion of test results indicating advanced HIV disease annually ranged from 14.5% in Uganda to 29.8% in Cameroon. 6.9% (95% CI: 6.8-7.0%) of test results showed very advanced HIV disease (CD4<100 cells/ul) in 2016. CONCLUSIONS:The proportion of CD4 test results indicating advanced disease was relatively high and consistent across four high HIV burden countries