英文标题：
《Explicit solutions to utility maximization problems in a
  regime-switching market model via Laplace transforms》
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作者：
Adriana Ocejo
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最新提交年份：
2018
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英文摘要：
  We study the problem of utility maximization from terminal wealth in which an agent optimally builds her portfolio by investing in a bond and a risky asset. The asset price dynamics follow a diffusion process with regime-switching coefficients modeled by a continuous-time finite-state Markov chain. We consider an investor with a Constant Relative Risk Aversion (CRRA) utility function. We deduce the associated Hamilton-Jacobi-Bellman equation to construct the solution and the optimal trading strategy and verify optimality by showing that the value function is the unique constrained viscosity solution of the HJB equation. By means of a Laplace transform method, we show how to explicitly compute the value function and illustrate the method with the two- and three-states cases. This method is interesting in its own right and can be adapted in other applications involving hybrid systems and using other types of transforms with basic properties similar to the Laplace transform.
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中文摘要：
我们研究了终端财富的效用最大化问题，在此问题中，代理人通过投资债券和风险资产最优地构建其投资组合。资产价格动态遵循一个扩散过程，制度转换系数由连续时间有限状态马尔可夫链建模。我们考虑一个具有常数相对风险厌恶（CRRA）效用函数的投资者。我们推导了相关的Hamilton-Jacobi-Bellman方程来构造解和最优交易策略，并通过证明值函数是HJB方程的唯一约束粘性解来验证最优性。通过拉普拉斯变换方法，我们展示了如何显式计算值函数，并用两态和三态情况说明了该方法。这种方法本身就很有趣，可以在涉及混合系统的其他应用中进行调整，并使用具有类似于拉普拉斯变换的基本特性的其他类型的变换。
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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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