Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
12-2025
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Robert M. Price, Rodney Keaton
Abstract
This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival and fertility transitions to classical life contingencies, thereby recovering survival functions, annual death probabilities, expected lifetime, and present values of life-contingent cash flows (Dickson, Hardy, & Waters, 2013)[ 3]. The result is a mathematically principled, empirically calibrated framework in which agent-level events aggregate to operator- level dynamics, so that actuarial analysis and simulation-based demography become formally consistent.
Document Type
Thesis - unrestricted
Recommended Citation
Kings, David, "A Leslie System for a Demographic Simulation: From an Actuarial Point of View" (2025). Electronic Theses and Dissertations. Paper 4640. https://dc.etsu.edu/etd/4640
Copyright
Copyright by David Kings
Included in
Algebra Commons, Applied Mathematics Commons, Applied Statistics Commons, Computer Sciences Commons, Data Science Commons, Discrete Mathematics and Combinatorics Commons, Longitudinal Data Analysis and Time Series Commons, Probability Commons, Statistical Models Commons, Survival Analysis Commons
