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雷达卡
英文标题：
《Sensitivity analysis for expected utility maximization in incomplete
Brownian market models》
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作者：
Julio Backhoff Veraguas and Francisco Silva
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最新提交年份：
2017
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英文摘要：
We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for utility functions of positive power-type. The method consists in moving the parameters through change of measure, which we call a weak perturbation, decoupling the usual wealth equation from the varying parameters. By rewriting the maximization problem in terms of a convex-analytical support function of a weakly-compact set, crucially leveraging on the work of Backhoff and Fontbona (SIFIN 2016), the previous formulation let us prove the Hadamard directional differentiability of the value function w.r.t. the drift and interest rate parameters, as well as for volatility matrices under a stability condition on their Kernel, and derive explicit expressions for the directional derivatives. We contrast our proposed weak perturbations against what we call strong perturbations, where the wealth equation is directly influenced by the changing parameters. Contrary to conventional wisdom, we find that both points of view generally yield different sensitivities unless e.g. if initial parameters and their perturbations are deterministic.
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中文摘要：
我们研究了不完全萨缪尔森模型中最终财富效用最大化问题的模型参数敏感性问题，主要（但不限于）正幂型效用函数。该方法包括通过测量值的变化来移动参数，我们称之为弱扰动，将通常的财富方程与变化的参数解耦。通过用弱紧集的凸分析支持函数重写最大化问题，关键是利用Backhoff和Fontbona（SIFIN 2016）的工作，前面的公式让我们证明了价值函数w.r.t.漂移和利率参数的Hadamard方向可微性，以及在其核上的稳定条件下的波动矩阵，并导出了方向导数的显式表达式。我们将我们提出的弱摄动与我们所称的强摄动进行对比，在强摄动中，财富方程直接受到变化参数的影响。与传统观点相反，我们发现这两种观点通常会产生不同的灵敏度，除非初始参数及其扰动是确定性的。
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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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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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