英文标题：
《Risk Sensitive Portfolio Optimization with Default Contagion and
Regime-Switching》
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作者：
Lijun Bo, Huafu Liao and Xiang Yu
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最新提交年份：
2018
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英文摘要：
We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function, we investigate the corresponding recursive infinite-dimensional nonlinear dynamical programming equations (DPEs) based on default states. We propose to work in the following procedure: Applying the theory of monotone dynamical system, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space. The associated optimal feedback strategy is characterized by developing a rigorous verification theorem. Building upon results in the first stage, we construct a sequence of approximating risk sensitive control problems with finite states and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs. The construction and approximation of the optimal feedback strategy for the original problem are also thoroughly discussed.
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中文摘要：
我们研究了一个存在违约传染的制度转换信贷市场中风险敏感投资组合配置的开放性问题。假设马尔可夫机制转换过程的状态空间是一个可数无限集。为了刻画值函数，我们研究了相应的基于默认状态的递归无限维非线性动态规划方程（DPE）。我们建议按照以下步骤进行工作：应用单调动力系统理论，首先在有限状态空间中通过截断变元建立递归DPE经典解的存在唯一性。相关的最优反馈策略的特点是发展了一个严格的验证定理。在第一阶段的结果的基础上，我们构造了一个具有有限状态的近似风险敏感控制问题序列，并证明了所得到的光滑值函数将收敛于原始DPEs系统的经典解。对原问题最优反馈策略的构造和逼近进行了深入的讨论。
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分类信息：

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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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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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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