Abstract and Applied Analysis

Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process

Liuwei Zhou and Zhijie Wang

Full-text: Open access

Abstract

The problem of a portfolio strategy for financial market with regime switching driven by geometric Lévy process is investigated in this paper. The considered financial market includes one bond and multiple stocks which has few researches up to now. A new and general Black-Scholes (B-S) model is set up, in which the interest rate of the bond, the rate of return, and the volatility of the stocks vary as the market states switching and the stock prices are driven by geometric Lévy process. For the general B-S model of the financial market, a portfolio strategy which is determined by a partial differential equation (PDE) of parabolic type is given by using Itô formula. The PDE is an extension of existing result. The solvability of the PDE is researched by making use of variables transformation. An application of the solvability of the PDE on the European options with the final data is given finally.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 538041, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605764

Digital Object Identifier
doi:10.1155/2014/538041

Mathematical Reviews number (MathSciNet)
MR3191050

Zentralblatt MATH identifier
07022578

Citation

Zhou, Liuwei; Wang, Zhijie. Portfolio Strategy of Financial Market with Regime Switching Driven by Geometric Lévy Process. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 538041, 9 pages. doi:10.1155/2014/538041. https://projecteuclid.org/euclid.aaa/1412605764


Export citation

References

  • H. Markowitz, “Portfolio selection,” Journal of Finance, vol. 7, pp. 77–91, 1952.
  • D. Li and W.-L. Ng, “Optimal dynamic portfolio selection: multiperiod mean-variance formulation,” Mathematical Finance, vol. 10, no. 3, pp. 387–406, 2000.
  • B. ${\text{\O}}$ksendal, Stochastic Differential Equations, Springer, 6th edition, 2005.
  • X. Guo and Q. Zhang, “Optimal selling rules in a regime switching model,” IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1450–1455, 2005.
  • M. Pemy, Q. Zhang, and G. G. Yin, “Liquidation of a large block of stock with regime switching,” Mathematical Finance, vol. 18, no. 4, pp. 629–648, 2008.
  • H. Wu and Z. Li, “Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon,” Journal of Systems Science & Complexity, vol. 24, no. 1, pp. 140–155, 2011.
  • H. Wu and Z. Li, “Multi-period mean-variance portfolio selection with regime switching and a stochastic cash flow,” Insurance: Mathematics & Economics, vol. 50, no. 3, pp. 371–384, 2012.
  • J. Kallsen, “Optimal portfolios for exponential Lévy processes,” Mathematical Methods of Operations Research, vol. 51, no. 3, pp. 357–374, 2000.
  • D. Applebaum, Lévy Processes and Stochastic Calculus, vol. 93, Cambridge University Press, Cambridge, UK, 2004.
  • N. Vandaele and M. Vanmaele, “A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market,” Insurance: Mathematics & Economics, vol. 42, no. 3, pp. 1128–1137, 2008.
  • C. Weng, “Constant proportion portfolio insurance under a regime switching exponential Lévy process,” Insurance: Mathematics & Economics, vol. 52, no. 3, pp. 508–521, 2013.
  • N. Bäuerle and A. Blatter, “Optimal control and dependence modeling of insurance portfolios with Lévy dynamics,” Insurance: Mathematics & Economics, vol. 48, no. 3, pp. 398–405, 2011.
  • K. C. Yuen and C. Yin, “On optimality of the barrier strategy for a general Lévy risk process,” Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 1700–1707, 2011. \endinput