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Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…
Human longevity leaders with remarkably long lifespan play a crucial role in the advancement of longevity research. In this paper, we propose a stochastic model to describe the evolution of the age of the oldest person in the world by a…
There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
How long people live depends on their health, and how it changes with age. Individual health can be tracked by the accumulation of age-related health deficits. The fraction of age-related deficits is a simple quantitative measure of human…
The significance of mortality modeling extends across multiple research areas, ranging from life insurance valuation to optimal lifetime decision-making. Existing approaches, such as mortality laws and factor-based models, often fall short…
A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…
The Gompertz-Makeham distribution, which is used commonly to represent lifetimes based on laws of mortality, is one of the most popular choices for mortality modelling in the field of actuarial science. This paper investigates ordering…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence…
The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic…
A robust multilevel functional data method is proposed to forecast age-specific mortality rate and life expectancy for two or more populations in developed countries with high-quality vital registration systems. It uses a robust multilevel…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
Mortality forecasting plays a pivotal role in insurance and financial risk management of life insurers, pension funds, and social securities. Mortality data is usually high-dimensional in nature and favors factor model approaches to…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…