Abstract
In the paper we propose a stochastic model, based on a Vasicek non-homogeneous diffusion process, in which the trend coefficient and the volatility are deterministic time-dependent functions. The stochastic inference based on discrete sampling in time is established using a methodology based on the moments of the stochastic process. In order to evaluate the goodness of the proposed methodology a simulation study is discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albano, G., Giorno, V., Román-Pomán, P., Torres-Ruiz, F.: Inference on a stochastic two-compartment model in tumor growth. Comp. Stat. Data Anal. 56, 1723–1736 (2012)
Albano, G., Giorno, V., Román, P., Román, S., Torres, F.: Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process. J. Theor. Biol. 364, 206–219 (2015)
Albano, G., Giorno, V., Roman-Roman, P., Torres-Ruiz, F.: On a non-homogeneous Gompertz-type diffusion process: inference and first passage time. In: Lecture Notes in Computer Science, vol. 10672, pp. 47–54. Springer (2018)
Chen, W., Xu, L., Zhu, S.P.: Stock loan valuation under a stochastic interest rate model. Comput. Math. Appl. 70, 1757–1771 (2015)
Di Lorenzo, E., Orlando, A., Sibillo, M.: Stochastic model for loan interest rates. Banks and Bank Syst. 8, 94–99 (2013)
Giorno, V., Román, P., Spina, S., Torres, F.: Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics. Comput. Stat. Data Anal. 107, 18–31 (2017)
Gutiérrez, R., Nafidi, A., Pascual, A.: Detection, modelling and estimation of non-linear trends by using a non-homogeneous Vasicek stochastic diffusion. Application to CO2 emissions in Morocco. Stoch. Environ. Res. Risk Assess. 26, 533–543 (2012)
Hull, J.: Options, Futures and Other Derivatives. Pearson, London (2000)
Spina, S., Giorno, V., Román, P., Torres, F.: A stochastic model of cancer growth subject to an intermittent treatment with combined effects. Bull. Math. Biol. 77(11), 2711–2736 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Albano, G., Giorno, V. (2018). Inference in a Non-Homogeneous Vasicek Type Model. In: Corazza, M., Durbán, M., Grané, A., Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-89824-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-89824-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89823-0
Online ISBN: 978-3-319-89824-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)