Optimal policies for discrete time risk processes with a Markov chain investment model

We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included

Inequalities for the ruin probability in a controlled discrete-time risk process

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included.Risk process, Ruin probability, Proportional reinsurance, Lundberg`s

Inequalities for the ruin probability in a controlled discrete-time risk process

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included

OPTIMAL POLICIES FOR DISCRETE TIME RISK PROCESSES WITH A MARKOV CHAIN INVESTMENT MODEL

We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included.

Genetic and environmental influences on eating behaviors in 2.5-and 9-year-old children: a longitudinal twin study

Peer reviewe

Dietary Intake at 9 Years and Subsequent Body Mass Index in Adolescent Boys and Girls : A Study of Monozygotic Twin Pairs

There is a lack of evidence pointing to specific dietary elements related to weight gain and obesity prevention in childhood and adulthood. Dietary intake and obesity are both inherited and culturally transmitted, but most prospective studies on the association between diet and weight status do not take genetics into consideration. The objective of this study was to document the association between dietary intake at 9 years and subsequent Body Mass Index (BMI) in adolescent monozygotic boy and girl twin pairs. This research used data from 152 twin pairs. Dietary data were collected from two 24-hour-recall interviews with a parent and the child aged 9 years. Height and weight were obtained when the twins were aged 9, 12, 13, and 14 years. Intrapair variability analysis was performed to identify dietary elements related to BMI changes in subsequent years. BMI-discordant monozygotic twin pairs were also identified to analyze the dietary constituents that may have generated the discordance. After eliminating potential confounding genetic factors, pre-adolescent boys who ate fewer grain products and fruit and consumed more high-fat meat and milk had higher BMIs during adolescence; pre-adolescent girls who consumed more grain products and high-fat meat and milk had higher BMIs during adolescence. Energy intake (EI) at 9 years was not related to BMI in subsequent years. Our study suggests that messages and interventions directed at obesity prevention could take advantage of sex-specific designs and, eventually, genetic information.Peer reviewe

Control de modelos Markovianos : una aproximación al problema de ruina

In this thesis the ruin probabilities in some controlled discrete-time risk processes with a Markov chain interest are studied. To reduce the risk of ruin there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included. It is shown that the problems considered can be imbedded in the framework of Markov decision problem but with some special features. We establish the dynamic programming algorithm in finite and infinite horizon cases for a general Markov Decision Process (MDP). Moreover, we provide conditions for the existences of measurable selectors. _____________________________________En este trabajo se estudia la probabilidad de ruina de algunos procesos de riesgo controlados en tiempo discreto que incluyan una cadena de Markov para las tasas de interés. Para reducir el riesgo de ruina existe la posibilidad de reasegurar parte o la totalidad del fondo de reservas. Se facilitan formulas recursivas y ecuaciones para calcular la probabilidad de ruina. Desigualdades generalizadas tipo Lundberg para la probabilidad de ruina son deducidas cuando consideramos una política estacionaria constante desde el inicio. Se analizan las relaciones entre las desigualdades halladas. Se incluyen algunos ejemplos numéricos para ilustrar estos resultados. Se muestra que los problemas considerados pueden ser vistos en el marco de los problemas de Decisión Markovianos. Se establecen algoritmos de programación dinámica para un modelo de Decisión Markoviano general en los casos de horizonte finito e infinito. Además, se muestran las condiciones necesarias para la existencia de selectores medibles

An exploration of reported food intake among inmates who gained body weight during incarceration in Canadian federal penitentiaries.

BACKGROUND:Canadian penitentiaries have recently been shown to be obesogenic. However, little is known about the eating habits of inmates who gained weight while living in the prison environment. METHODS:This retrospective cohort study examined the reported food intake of inmates during incarceration in federal penitentiaries. During a face to face interview, anthropometric measures (2016-2017) were taken and compared to anthropometric data at the beginning of incarceration (mean follow-up of 5.0 ± 8.3 years). Self-reported data on food intake were collected via a food frequency questionnaire. RESULTS:Inmates who gained the most weight (15.7 kg) during incarceration reported not eating vegetables. They were followed by inmates who gained 14.3 kg and reported not eating fruit. Other inmates who gained a significant amount of weight reported not eating cereal, dairy or legumes. Moreover, inmates' weight gain was also assessed by special diets: inmates following a religious diet (4.5 kg) or a diet of conscience (-0.3 kg) gained less weight than inmates not following a diet (5.8 kg). In comparison to other types of diets, inmates on a medical diet gained the most weight (7.5 kg). Furthermore, inmates who gained significant weight (8.0 kg) also reported not purchasing healthy foods from the commissary store (or "canteen"), whereas inmates who gained less weight (4.8 kg) reported purchasing healthy foods from the commissary store (or "canteen"). The observed weight gain was positively associated with food purchased from the commissary store (or "canteen"), but was not associated with the feeding system of the penitentiary (tray, cafeteria or meal plan). DISCUSSION:Food intake during incarceration is a modifiable risk factor that could be the target of weight management interventions with inmates. Our findings suggest that inmates who gained the most weight also reported having low intake of foods deemed healthy (vegetables, fruit, cereal, dairy and legumes) from food services and from the commissary store (or "canteen") purchases