Markov (Set) chains application to predict mortality rates using extended Milevsky-Promislov generalized mortality...

Area of Science:

• Actuarial science
• Mathematical statistics
• Demography

Background:

• Mortality rates are fundamental for actuarial calculations, including life insurance premiums and life expectancy.
• Accurate modeling and forecasting of mortality rates are essential for financial risk assessment.
• Existing models, such as the Lee-Carter model, have limitations in precisely forecasting mortality trends.

Purpose of the Study:

• To propose a new method for modeling and forecasting mortality rates.
• To enhance the precision of mortality rate forecasts compared to conventional models.
• To utilize stochastic switch models with polynomial excitations and Markov chains for mortality modeling.

Main Methods:

• The study employs stochastic Milevsky-Promislov switch models with excitations.
• Excitations are modeled using polynomial outputs (2nd, 4th, 6th order) from a non-Gaussian Linear Scalar Filter (nGLSF).
• A Markov (Set) chain, with states defined by even orders of the nGLSF polynomial, is incorporated.

Main Results:

• The proposed model's order determines theoretical death rate values.
• The model provides a more precise forecast of mortality rates than the Lee-Carter model.
• The integration of nGLSF polynomial outputs and Markov chains enhances predictive accuracy.

Conclusions:

• The novel stochastic model offers a more accurate approach to forecasting mortality rates.
• This method has significant implications for the accuracy of life expectancy calculations and insurance premium setting.
• The findings suggest a superior alternative to the widely used Lee-Carter model for mortality forecasting.