https://link.springer.com/content/pdf/10.1057%2Fjors.1968.81.pdf

Stochastic Models for Social Processes

Probability Tools For Stochastic Modelling.- Renewal Theory and Markov Chains.- Markov Renewal Processes, Semi-Markov Processes and Markov Random Walks.- Discrete Time and Reward Smp and their Numerical Treatment.- Semi-Markov Extensions of the Black-Scholes Model.- Other Semi-Markov Models in Finance and Insurance.- Insurance Risk Models.- Reliability and Credit Risk Models.- Generalised Non-Homogeneous Models for Pension Funds and Manpower Management.

Semi-Markov Risk Models for Finance, Insurance and Reliability

Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. * Clearly defines the properties and theorems from discrete state Semi-Markov Process (SMP) theory.* Describes the method behind constructing Semi-Markov (SM) models and SM decision models in the field of reliability and maintenance.* Provides numerous individual versions of SM models, including the most recent and their impact on system reliability and maintenance.

Semi-Markov Processes: Applications in System Reliability and Maintenance

In this paper, we define a discrete-time semi-Markov model and propose a computation procedure for solving the corresponding Markov renewal equation, necessary for all our reliability measurements. Then, we compute the reliability and its related measures, and we apply the results to a three-state system.

Discrete-Time Semi-Markov Model for Reliability and Survival Analysis

In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

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Discrete Time Non-Homogeneous Semi-Markov Processes Applied to Models for Disability Insurance

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system. STOCHASTIC POPULATION MODELS; SEMI-MARKOV PROCESS; MANPOWER SYSTEMS; NON-HOMOGENEOUS MARKOV CHAINS AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 90B70 SECONDARY 60J20

Non-homogeneous semi-Markov systems and maintainability of the state sizes

Asymptotic behavior of nonhomogeneous semi-Markov systems

In the present paper, the reward paths in non homogeneous semi-Markov systems in discrete time are examined with stochastic selection of the transition probabilities. The mean entrance probabilities and the mean rewards in the course of time are evaluated. Then the rate of the total reward for the homogeneous case is examined and the mean total reward is evaluated by means of p.g.f’s.

Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities

In the present we introduce and define the non-homogeneous semi-Markov system in continuous time. We study the problem of finding the expected population structure in closed analytic form, in relation with the basic sequences of the system. Moreover, the problem of the asymptotic behavior of the system is studied under certain conditions. We first study the limiting behavior of the imbedded non-homogeneous semi-Markov chain and then we provide the asymptotic population structure in closed analytic form.

Continuous Time Non Homogeneous Semi-Markov Systems

Previously, continuous time Markov and semi-Markow models have been developed for a multi-grade system with a number of transient states and a single absorbing state. Such systems have been studied with Poisson arrivals with known growth. Such models have been applied to manpower planning and the movement of patients through a hospital system. In this paper, we develop a reward model for a discrete time homogeneous semi-Markov system with Poisson arrivals and the same model where the system has growth with known size at each time point. Discrete time is employed here to accommodate a discrete reward structure. Results are obtained for the distribution, and mean of daily rewards of such system at any time, and in steady state; the expected reward in a period of time is also determined. These results are illustrated using data on employees moving through a company hierarchy and data for hospital patients.

Aleka A. Papadopoulou

Papers

Non-homogeneous semi-Markov systems and maintainability of the state sizes

Asymptotic behavior of nonhomogeneous semi-Markov systems

Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities

Continuous Time Non Homogeneous Semi-Markov Systems

Discrete Time Reward Models for Homogeneous Semi-Markov Systems