Mixed distributions with applications in finance and actuarial science
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Authors
Amponsah, Charles Kwame
Issue Date
2021
Type
Dissertation
Language
Keywords
Actuarial Science , EM Algorithm , Finance , Maximum Likelihood Estimation , Mixed Distributions , Random Sums
Alternative Title
Abstract
We study distributions connected with joint events (X, N), where X is the sum of N non-negative random variables {Xi}, which may be dependent or independent of N, and joint events (X, N, Y, M). In the latter, the X and Y are the sums of N and M non-negative random variables {Xi} and {Yi}, respectively. Models of this kind arise quite naturally in severalareas such as finance, actuarial science, hydro-climatic studies and others. In finance, the quantity N may represents a duration of growth in value of an investment, where a group of consecutive values of log-returns are of the same positive sign and X is its cumulative log-return. Inturn, the quantity M may represents a duration of decline in value of an investment, where a group of consecutive values of log-returns are of the same negative sign and Y is its cumulative log-return. In actuarial science, the N represents claim frequency and X represents the aggregate claim amount in a given time period. In clinical studies, N represents the number of hospital visits and X corresponds to the cumulative hospitalization cost. Our results include generalizations and formulation of bivariate and multivariate distributions that go beyond already existing models. In addition to theoretical results, we also consider the practical problem of parameter estimation using maximum likelihood, E-M algorithms, and simulation studies to validate our estimation strategies and applications
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Creative Commons Attribution-ShareAlike 4.0 United States