Global hedging in incomplete markets

最近的金融危机凸显了健全的风险管理做法对金融机构避免财务困难和破产的重要性。金融衍生品的对冲是金融机构最关心的问题；这些产品具有复杂的风险，可以在短时间内导致极端损失。我的研究计划侧重于套期保值程序，适用于现实的不完全市场框架，其中风险不能完全消除。更准确地说，我的计划旨在促进一种被称为全球对冲的特定类别对冲计划的发展。全球对冲计划最大限度地降低风险，直至对冲到期。这代表了传统短视方法的概念优势，如delta对冲和局部风险最小化，这些方法只考虑到下一个时间段的风险。这就解释了为什么全球对冲方法比本地对冲方法表现出更高的绩效，参见franois等人（2012）、Godin（2015）和Augustiniak等人（2016）。****虽然全球对冲方案更有效，但目前它们的使用受到其较高复杂性的阻碍。事实上，全局对冲模型涉及最优随机控制来优化对冲策略。由于相关的繁重的数值负担，这些过程的数值实现是非平凡的。我的研究计划的主要长期目标是促进全球对冲模型的发展，使其能够在更广泛的实际设置中应用，并促进其实施。这一目标将通过三个主要的研究途径来实现：(i)开发更有效的数值算法，可以加快全球对冲的运行时间。将研究的方案示例包括谱插值，模拟和回归以及决策后状态变量动态规划。（ii）量化全球套期保值优于传统本地方法的表现，并评估各种市场背景下剩余风险的大小。在更广泛的范围内制订套期保值计划，考虑到现有方法目前未考虑到的额外风险。这些风险包括流动性风险和波动面风险。*有效套期保值程序的发展应使经验丰富的投资者和金融机构受益，使他们能够显著降低风险状况，从而降低他们破产的可能性。**

The recent financial crisis highlighted the importance of sound risk management practices for financial institutions to avoid financial hardship and bankruptcy. The hedging of financial derivatives is a prime concern for financial institutions; these products entail complex risks which can lead to extreme losses in a short amount of time. My research program focuses on hedging procedures which apply in realistic incomplete market frameworks where risk cannot be completely eliminated. More precisely, my program aims at contributing to the development of a specific category of hedging schemes referred to as global hedging. Global hedging schemes minimize risk up to the maturity of the hedge. This represents a conceptual advantage over traditional myopic methods such as delta-hedging and local risk-minimization which only consider risk up to the next time period. This explains why global hedging methods were shown to exhibit a higher performance than their local counterparts, see François et al. (2012), Godin (2015) and Augustiniak et al. (2016).****Although global hedging schemes are more efficient, their use is currently hindered by their higher complexity. Indeed, global hedging models involve optimal stochastic control to optimize hedging policies. The numerical implementation of such procedures is non-trivial because of the associated heavy numerical burden. The main long term objective of my research program is to contribute to the development of global hedging models to allow their application in a wider number of practical setups and to facilitate their implementation. This objective will be realized through three main research avenues: (i) Developing more efficient numerical algorithms which can accelerate the running time of global hedging. Examples of schemes that will be investigated include spectral interpolation, simulation and regression and post-decision state variables dynamic programming. (ii) Quantifying the outperformance of global hedging over traditional local methods and assessing the magnitude of residual risk in various market contexts. (iii) Developing hedging schemes in broader contexts considering additional risks that are not currently taken into account by existing methods. Such risks include liquidity risk and volatility surface risk.*The development of efficient hedging procedures should benefit sophisticated investors and financial institutions by allowing them to significantly reduce their risk profile, thus decreasing the probability they become insolvent.**