摘要翻译：
本文在控制区域为凸的前提下，建立并研究了正反向随机Volterra积分方程的随机极大值原理。然后给出了倒向随机Volterra积分方程的线性二次型最优控制问题。基于解决上述问题的技术技巧，提出了一种更为简便、简洁的求解BSVIEs问题的M-解唯一可解性的方法。最后，利用最大值原理研究了FBSVIES的风险最小化问题。在某些特殊情况下得到了闭式最优投资组合。
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英文标题：
《A maximum principle for forward-backward stochastic Volterra integral
  equations and applications in finance》
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作者：
Tianxiao Wang and Yufeng Shi
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present to illustrate the aforementioned optimal control problem. Motivated by the technical skills in solving above problem, a more convenient and briefer method for the unique solvability of M-solution for BSVIEs is proposed. At last, we will investigate a risk minimization problem by means of the maximum principle for FBSVIEs. Closed-form optimal portfolio is obtained in some special cases.
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PDF链接：
https://arxiv.org/pdf/1004.2206