Skip to main content

Inference in a Non-Homogeneous Vasicek Type Model

  • Chapter
  • First Online:
Mathematical and Statistical Methods for Actuarial Sciences and Finance
  • 2691 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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)

    Article  MathSciNet  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. 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)

    Chapter  Google Scholar 

  4. Chen, W., Xu, L., Zhu, S.P.: Stock loan valuation under a stochastic interest rate model. Comput. Math. Appl. 70, 1757–1771 (2015)

    Article  MathSciNet  Google Scholar 

  5. Di Lorenzo, E., Orlando, A., Sibillo, M.: Stochastic model for loan interest rates. Banks and Bank Syst. 8, 94–99 (2013)

    Google Scholar 

  6. 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)

    Article  MathSciNet  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Hull, J.: Options, Futures and Other Derivatives. Pearson, London (2000)

    Google Scholar 

  9. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giuseppina Albano .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

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

Publish with us

Policies and ethics