Ανάλυση από κοινού ασφαλίσεων ζωής σε περιβάλλον με στοχαστικά επιτόκια
This thesis deals with the study of group life insurance policies in a stochastic interest rate environment. Joint life insurance could be suitable, for example, for a married couple, family or employees in a company. The need of stochastic models of interest rates arises from the fact that the assumption of interest rate independence from period to period is not realistic. Chapter one is an introductory section provides a literature review concerning models of policyholders' survivorship from individuals to pairs, and also models for stochastic interest rates were proposed in the actuarial practice. Both components are essential in the valuation of joint life insurance. Chapter two describes in detail the stochastic interest rate assumptions considering the discrete time stochastic AR(1) model, and the decrement according to life insurance theory. Under the Gompertz mortality law, the independent model of mortality is analyzed and two models of dependent mortality, namely copula and common shock are considered regarding policy coverage for two individuals. Chapter three, under the joint first-to-die policy, studies the valuation of a two-person group insurance policy and a general portfolio of such policies and gives expressions for the first two moments of the prospective loss random variable. Two approaches are followed, namely the individual loss random variable and the annual stochastic cash flows. Finally, the analysis of the total portfolio risk in terms of insurance risk and investment risk is discussed. Chapter four performs similar analysis for a single policy issued to a pair at the age (x, y) under joint last-to-die insurance, and for portfolio with a number of such policies. The fifth chapter investigates through a numerical application the joint first-to-die insurance policy model under the AR(1) stochastic interest rate model for an individual insurance policy and for a homogeneous portfolio. The tool of Mathematica wa used in analysis. Finally, chapter six summarizes the work.