Optimal portfolios based on weakly dependent data
Optimal portfolios based on weakly dependent data
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DOI：
10.3934/proc.2015.1041
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发表时间：
2015-11
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通讯作者：
Hiroshi Takahashi;Tatsuhiko Saigo;S. Kanagawa;K. Yoshihara
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文献类型：
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作者：
Hiroshi Takahashi;Tatsuhiko Saigo;S. Kanagawa;K. Yoshihara
设$\{\xi_k，k= 1，2，\ldots\}$是满足强混合条件的中心$d$维随机向量的严格平稳序列。利用$\{\xi_k\}$，我们考虑了由$d$股票组成的具有随机波动率和随机趋势的随机差分方程，并证明了一个收敛定理。在一维情形下，该差分方程的解几乎必然收敛于Black-Scholes型模型。本文的目的是将结果推广到多维情况。利用这个结果，我们得到了具有随机波动率的$d$股票价格模型的近似解。我们还给出了模型的最优投资组合的例子。
Let $\{\xi_k, k=1,2, \ldots\}$ be a strictly stationary sequence of centered $d$-dimensional random vectors satisfying the strong mixing condition. Using $\{\xi_k\}$, we consider a stochastic difference equation with a random volatility composed by $d$ stocks and a random trend and show a convergence theorem. In the one-dimensional case, the solution of this difference equation converges almost surely to a Black-Scholes type model. The purpose of this paper is to extend the results to multi-dimensional cases. Using the result, we obtain an approximations of $d$ stocks prices models with random volatilities. We also give examples of optimal portfolios for the models.