A class of portfolio selection with a four-factor futures price model |
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Authors: | Wei Yan and Shurong Li |
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Institution: | (1) Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China;(2) College of Information and Control Engineering, China University of Petroleum, Dongying Shandong, 257061, China |
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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. |
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Keywords: | Four-factor model Multi-period semi-variance portfolio Exchange rate Futures Numerical algorithm |
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