英文标题：
《Convex Hedging in Incomplete Markets》
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作者：
Birgit Rudloff
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最新提交年份：
2016
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英文摘要：
In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by F\\\"ollmer, Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim $\\widetilde{\\varphi}H$, where $H$ is the payoff of the claim and $\\widetilde{\\varphi}$ is the solution of the static optimization problem, the optimal randomized test. In this paper, we will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical $0$-$1$-structure.
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中文摘要：
在不完备的金融市场中，并非每一项未定权益都可以通过自筹资金战略复制。由此产生的短缺风险可以通过凸风险度量来衡量，最近由F \\“ollmer，Schied（2002）提出。寻找使短缺凸风险最小化的自筹资金策略的动态优化问题可分为静态优化问题和表示问题。因此，最优策略包括对修改后的索赔$\\widetilde{\\varphi}H$，其中$H$是索赔的报酬，$\\widetilde{\\varphi}$是静态优化问题的解决方案，即最优随机测试。在本文中，我们将利用凸对偶方法推导静态问题的最优性的充要条件。静态优化问题的解决方案是一个具有典型$0$-$1$-结构的随机测试。
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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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