摘要翻译：
研究了有界区域上抛物型倒向随机偏微分方程在矫顽力条件不一定满足且方程可以退化的情况下。提出了基于表示定理的一些广义解。除了在终端时刻具有标准Cauchy条件的问题外，还考虑了具有特殊非局部边界条件的问题。这些非局部条件将解决方案的终端值与整个过去解决方案的函数连接起来。得到了唯一性、可解性和正则性结果。讨论了在投资组合选择问题中的一些应用。
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英文标题：
《Degenerate backward SPDEs in domains: non-local boundary conditions and
  applications to finance》
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作者：
Nikolai Dokuchaev
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最新提交年份：
2014
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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：Mathematics        数学
二级分类：Analysis of PDEs        偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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英文摘要：
  Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a standard Cauchy condition at the terminal time, problems with special non-local boundary conditions are considered. These non-local conditions connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability and regularity results are obtained. Some applications to portfolio selection problem are considered.
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PDF链接：
https://arxiv.org/pdf/1211.5858