Abstract
Pathwise comparison results for controlled arithmetric Brownian motion processes and for controlled log-normal, also called logarithmic Brownian motion, processes are obtained. Applications of these results to finance are given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ikeda, N. and Watanabe, S. (1977), A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math. 14, 619–633.
Ferreyra, G. and Sundar, P. (1997), Comparison of solutions of stochastic equations and applications, submitted. Available at http://math.lsu.edu/TigerNotes/1998/VOL98.html
Fleming, W. H. and Soner, H. M. (1993), Controlled Markov Processes and Viscosity Solutions, Appl. Math., vol 25, Springer-Verlag, New York.
Gal’chuk, L. I. and Davis, M. H. A. (1981/82), A note on a comparison theorem for equations with different diffusions, Stochastics 6, 147–149.
Hojgaard, B. and Taksar, M. (1998), Controlling risk exposure and dividends pay-out schemes: Insurance company example, preprint.
O’Brien, G. L. (1980), A new comparison theorem for solutions of stochastic differential equations, Stochastics 3, no. 4, pp. 245–249.
Protter, P. (1990), Stochastic Integration and Differential Equations, Appl. Math., vol 21, Springer-Verlag, New York.
Taksar, M. and Zhou, Xun Yu, (1997), In Proceedings of the 36th Conference on Decision and Control, San Diego, CA, Dec 10-12, 1997, pp. 2791–2794.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ferreyra, G., Sundar, P. (1999). Pathwise Comparison of Arithmetric Brownian Motions and Log-normal Processes. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_32
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1784-8_32
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
Online ISBN: 978-1-4612-1784-8
eBook Packages: Springer Book Archive