Skip to main content
Log in

A class of portfolio selection with a four-factor futures price model

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution of the PDE with parameters is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markowitzs portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. Then, a continuous-time mean-variance portfolio model is also considered. The corresponding stochastic Hamilton-Jacobi-Bellman (HJB) equation of the problem with nonlinear constraints is derived. A numerical algorithm is proposed for finding the optimal solution in this paper. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, the fuel futures in Shanghai exchange market and the Brent crude oil futures in London exchange market are selected to be examples.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bjerksund, P. (1991). Contingent claims evaluation when the convenience yield is stochastic: analytical results. Working paper.

  • Cortazar, G., & Schwartz, E. S. (1994). The valuation of commodingent claims. The Journal of Derivatives, 4(1), 27–39.

    Google Scholar 

  • Cortazar, G., & Schwartz, E. S. (2003). Implementing a stochastic model for oil futures prices. Energy Economics, 25(1), 215–238.

    Article  Google Scholar 

  • Cox, J. C., & Ross, S. A. (1985). The valuation of options for alternation stochastic process. Journal of Financial Economics, 3(1), 145–166.

    Article  Google Scholar 

  • Fleming, W. H., & Soner, H. M. (1992). Controlled Markov processes and viscosity solutions. New York: Springer.

    Google Scholar 

  • Gibson, R., & Schwartz, E. S. (1990). Stochastic convenience yield and the pricing of oil contingent claims. Journal of Finance, XLV(4), 959–976.

    Article  Google Scholar 

  • Gong, G. L. (1987). Introduction to stochastic differential equations. Peking: Peking University Press.

    Google Scholar 

  • Grauer, R. R., & Hakansson, N. H. (1993). On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies. Management Science, 39(7), 856–871.

    Article  Google Scholar 

  • Guo, W. J., & Xu, C. M. (2004). Optimal portfolio selection when stock prices follow an jump-diffusion process. Mathematical Methods of Operations Research, 60(2), 485–496.

    Google Scholar 

  • Hakansson, N. H. (2001). Multi-period mean-variance analysis: toward a general theory of portfolio choice. Journal of Finance, 26(4), 857–884.

    Article  Google Scholar 

  • Hogar, W. W., & Warren, J. M. (1974). Toward the development of an equi1ibrium capital market model based on semivariance. Journal of Financial and Quantitative Analysis, 9(1), 1–11.

    Article  Google Scholar 

  • Jarrow, R. A., & Rudd, A. (1983). Option pricing. Homewood: Richard D. Irwin Press.

    Google Scholar 

  • Lanzilotti, R. F. (1958). Pricing objectives in large companies. American Economic Revies, 48(4), 921–940.

    Google Scholar 

  • Li, X., Zhou, X. Y., & Lim, A. E. B. (2002). Dynamic mean-variance portfolio selection with no-shorting constraints. SIAM Journal on Control and Optimization, 40(5), 1540–1555.

    Article  Google Scholar 

  • Lim, A. E. B., & Zhou, X. Y. (2002). Mean-variance portfolio selection with random parameters in a complete market. Mathematics of Operations Research, 27(1), 101–120.

    Article  Google Scholar 

  • Mao, J. C. T. (1970). Models of capital budgeting, E-V versus E-S. Journal of Financial and Quantitative Analysis, 4(3), 557–675.

    Google Scholar 

  • Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.

    Article  Google Scholar 

  • Markowitz, H. (1959). Portfolio selection. New York: Wiley.

    Google Scholar 

  • Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics, 51(2), 247–257.

    Article  Google Scholar 

  • Merton, R. C. (1971). Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(2), 373–413.

    Article  Google Scholar 

  • Merton, R. C. (1990). Continuous-time finance. Cambridge: Basil Blackwell Press.

    Google Scholar 

  • Mossin, J. (1968). Optimal multiperiod portfolio policies. Journal of Business, 41(2), 215–229.

    Article  Google Scholar 

  • Petty, J. W., Scott, D. F., & Monroe, M. B. (1975). The capital expenditure decision-makinq process of large corporations. Engineering Economist, 20(1), 159–172.

    Article  Google Scholar 

  • Pliska, S. R. (1997). Introduction to Mathematical Finance. Malden: Blackwell.

    Google Scholar 

  • Ross, S. A. (1995). Hedging long run commitments: exercises in incomplete market pricing. Preliminary draft. Working paper.

  • Samuelson, P. A. (1969). Lifetime portfolio selection by dynamic stochastic programming. The Review of Economics and Statistics, 51(2), 239–246.

    Article  Google Scholar 

  • Schwartz, E. S. (1997). The stochastic behavior of commodity prices: implications for valuation and hedging. The Journal of Finance, LII(4), 923–973.

    Article  Google Scholar 

  • Schwartz, E. S., & Smith, J. E. (2000). Short-term variations and long-term dynamics in commodity prices. Management Science, 46(6), 893–911.

    Article  Google Scholar 

  • Sun, M. (1997). Domain decomposition algorithms for solving Hamilton-Jacobi-bellman equations. Numerical Functional Analysis and Optimization, 14(1), 145–166.

    Article  Google Scholar 

  • Swalm, R. O. (1966). Utility theory—insights into risk taking. Harvard Business Review, 44(1), 123–136.

    Google Scholar 

  • Yan, W., Miao, R., & Li, S. (2007). Multi-period semi-variance portfolio selection: model and numerical solution. Applied Mathematics and Computation, 194(1), 128–134.

    Article  Google Scholar 

  • Zhou, X. Y., & Li, X. (1997). Stochastic verification theorems within the framework of viscosity solutions. SIAM Journal on Control and Optimization, 35(1), 243–253.

    Article  Google Scholar 

  • Zhou, X. Y., & Li, D. (2000). Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Applied Mathematics and Optimization, 42(1), 19–33.

    Article  Google Scholar 

  • Zhou, S., & Zhan, W. (2003). A new domain decomposion method for an HJB equation. Journal of Computational and Applied Mathematics, 159(1), 195–204.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wei Yan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yan, W., Li, S. A class of portfolio selection with a four-factor futures price model. Ann Oper Res 164, 139–165 (2008). https://doi.org/10.1007/s10479-008-0398-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-008-0398-y

Keywords

Navigation