STOCHASTIC DIFFERENTIAL EQUATION: AN APPLICATION TO MORTALITY DATA
DOI:
https://doi.org/10.29121/granthaalayah.v8.i6.2020.538Keywords:
Stochastic Differential Equation, Mortality, Estimation, Confidence Interval, PredictionAbstract [English]
In the present paper we consider an application of stochastic differential equation to model age-specific mortalities. We use New Zealand mortality data for the period 1948–2015 to fit the model. The point predictions of mortality rates at ages 40, 60 and 80 are quite good, almost undistinguishable from the true mortality rates observed.
Downloads
References
Aït-Sahalia, Y. (2002). Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Comment. Journal of Business and Economic Statistics. 20(3):317-21 DOI: 10.1198/073500102288618405
Aït-Sahalia, Y. (2008). Closed-form likelihood expansions for multivariate diffusions. Ann. Statist. 36 (2008), no. 2, 906--937. doi:10.1214/009053607000000622. https://projecteuclid.org/euclid.aos/ DOI: https://doi.org/10.1214/009053607000000622
1205420523
Braumann, C.A. (1993) Model fitting and prediction in stochastic population growth models in random environments. Bulletin of the International Statistical Institute, LV (CP1), 163–164. Braumann, C.A. (1999a) Comparison of geometric Brownian motions and applications to population growth and finance. Bulletin of the International Statistical Institute, LVIII (CP1), 125–126.
Braumann, C. A., Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance, John Wiley & Sons Ltd, 2019. DOI: https://doi.org/10.1002/9781119166092
Itô, K. (1951) On Stochastic Differential Equations, American Mathematical Society Memoirs, No. 4. DOI: https://doi.org/10.1090/memo/0004
Kessler,M., Lindner A. and, Sorensen, M. Statistical Methods for Stochastic Differential Equations, Chapman and Hall/CRC, 2012. DOI: https://doi.org/10.1201/b12126
Lagarto, S. and Braumann, C.A. Modeling human population death rates: A bi-dimensional stochastic Gompertz model with correlated Wiener processes, in New Advances in Statistical Modeling and Applications (eds, A. Pacheo, R. Santos, M.R. Oliveira, and C.D. Paulino), Springer, Heidelberg, pp. 95–103, doi:10.1007/978-3-319-05323-3_9, 2014. DOI: https://doi.org/10.1007/978-3-319-05323-3_9
Øksendal, B. Stochastic Differential Equations. An Introduction with Applications, 6th edition, Springer, New York, 2003. DOI: https://doi.org/10.1007/978-3-642-14394-6_5
Talawar, A. S. and Agadi, R.P. (2020). Novel corona virus pandemic disease (covid-19): Some applications to south asian countries. International Journal of Research and Analytical Reviews, 7(2), 905-912.
Published
How to Cite
Issue
Section
License
With the licence CC-BY, authors retain the copyright, allowing anyone to download, reuse, re-print, modify, distribute, and/or copy their contribution. The work must be properly attributed to its author.
It is not necessary to ask for further permission from the author or journal board.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.
