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

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  • Wei Yan
  • Shurong Li

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. Copyright Springer Science+Business Media, LLC 2008

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  • Wei Yan & Shurong Li, 2008. "A class of portfolio selection with a four-factor futures price model," Annals of Operations Research, Springer, vol. 164(1), pages 139-165, November.
    • Handle: RePEc:spr:annopr:v:164:y:2008:i:1:p:139-165:10.1007/s10479-008-0398-y
    DOI: 10.1007/s10479-008-0398-y
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    Cited by:

    1. Sabri Boubaker & Zhenya Liu & Yaosong Zhan, 2022. "Risk management for crude oil futures: an optimal stopping-timing approach," Annals of Operations Research, Springer, vol. 313(1), pages 9-27, June.
    2. Junhe Chen & Marcos Escobar-Anel, 2021. "Model uncertainty on commodity portfolios, the role of convenience yield," Annals of Finance, Springer, vol. 17(4), pages 501-528, December.
    3. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    4. Jun Deng & Huifeng Pan & Shuyu Zhang & Bin Zou, 2021. "Optimal Bitcoin trading with inverse futures," Annals of Operations Research, Springer, vol. 304(1), pages 139-163, September.

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