英文标题：
《Viscosity properties with singularities in a state-constrained expected
utility maximization problem》
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作者：
Mourad Lazgham
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最新提交年份：
2015
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英文摘要：
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic programming principle, which allows us to derive conditions under which a classical solution of the HJB equation coincides with our value function (provided that it is smooth enough). On the other hand, we establish a comparison principle, which allows us to characterize our value function as the unique viscosity solution of the HJB equation.
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中文摘要：
我们考虑了源于有限燃料约束下的期望效用最大化问题的值函数，并证明了它与具有奇异性的非线性抛物退化Hamilton-Jacobi-Bellman（HJB）方程的密切关系。一方面，我们基于动态规划原理给出了一个所谓的验证论证，它允许我们推导出HJB方程的经典解与我们的值函数一致的条件（前提是它足够光滑）。另一方面，我们建立了一个比较原理，它允许我们将我们的值函数描述为HJB方程的唯一粘度解。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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