Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T12:45:20.768Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

Published online by Cambridge University Press:  29 August 2014

Terence Chan
Terence Chan*
Affiliation:
Dept. of Actuarial Mathematics and Statistics, Heriot-Watt University
*
Dept. of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH 14 4AS, U.K.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

Keywords

Lévy processBrownian motionstochastic investment model
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 77 - 93
Copyright
Copyright © International Actuarial Association 1998

References

Hürlimann, W. (1992), “Numerical evaluation of the Wilkie inflation model”, Insurance: Mathematics & Economics 11, 311–314.Google Scholar
Janicki, A. and Weron, A. (1993), Simulation and Chaotic Behaviour of α-Stable Stochastic Processes, Marcel Dekker.Google Scholar
Kloeden, P.E. and Platen, E. (1992), Numerical Solution of Stochastic Differential Equations, Springer.CrossRefGoogle Scholar
Protter, P. (1990), Stochastic Integration and Differential Equations, Springer.CrossRefGoogle Scholar
Rogers, L.C.G. and Williams, D. (1987), Diffusions, Markov Processes and Martingales, Vol. 2: Itô Calculus, Wiley.Google Scholar
Wilkie, A.D. (1986), “A stochastic investment model for actuarial use”, Trans. Faculty of Actuaries 39, 341–373.CrossRefGoogle Scholar
Wilkie, A.D. (1995), “More on a stochastic investment model for actuarial use”, British Actuarial Journal 1, 777–964.CrossRefGoogle Scholar