Robust Optimizations For Equity-Linked Products

这项提议的主要目标是为股权挂钩产品(ELP)制定稳健的对冲策略。ELPS形成了一类保险产品，在提供预先确定的担保金额的同时，有限地参与股票指数(股票指数年金)或共同基金(可变年金)的业绩。ELP被认为是一种长期金融衍生品，包括死亡、退保、退出和/或积累担保。在分析这些担保背后的风险时，Augustiniak&Boudreault(2012)研究了几个计量经济学模型，并使用金融危机(以及相关的股权挂钩收益)作为样本内期间，对这些模型进行了样本外分析。他们观察到，尾部风险衡量标准在不同的模型中存在显著差异。这强调了在对冲投资担保时谨慎选择模型的重要性。鉴于加拿大精算师学会建议使用随机模型来拨备不良贷款的未来损失，重要的是要有一种衡量标准，可以作为保险公司和监管机构在比较各种模型时的标尺，因此考虑采用稳健的方法来评估不良贷款。我建议推导出最坏情况下的套期保值策略和稳健控制方法。这两个概念都是对Gaillardetz&Hacem(2019)提出的风险控制战略的稳健适应。Osei Mireku*(2019)研究了当CVaR用于约束时的稳健对手套期保值策略。他通过抽样概率质量函数的不同不确定性集来给出近似解。我打算研究其他方法(例如数值方法)，因为模拟结果并不一致。朱和福岛(2009)将最坏情况局部CVaR的概念应用于投资组合管理。Gaillardetz&Hacem(2019)表明，通过最小化局部CVaR获得的套期保值策略优于基于一致动态风险度量的策略，该策略在最小化局部CVaR的同时惩罚未来的损失。我建议应用朱和福岛(2009)的结果，得出最坏情况下的一致性动态风险度量。我建议研究稳健的套期保值策略，其中风险度量被风险控制策略中的非随机度量所取代。这些都概括了代价高昂的超级复制策略，在这种策略中，不允许出现积极的损失。非随机测量可能会承认一些正的损失，但通过施加约束来抑制它们。基于Ben-Tal等人的结果。如(2009)所述，可使用计算上易于处理的等值重新公式来放宽基本财务过程中的离散假设。放松假设是一个有界的连续金融过程，通常使用一些上界和下界进行约束。在这种情况下，解可以用极值的凸组合来表示。

The main objective of this proposal is to develop robust hedging strategies for equity-linked products (ELPs). ELPs form a class of insurance products that offer limited participation in the performance of an equity index (Equity-indexed Annuity) or a mutual fund (Variable Annuity) while providing a predetermined guaranteed amount. ELPs are considered as long-term financial derivatives that include death, surrender, withdrawal, and/or accumulation guarantees. In analyzing the risk underlying these guarantees, Augustyniak & Boudreault (2012) study several econometric models and conduct out-of-sample analyses of these models, using the financial crisis (and the associated observed equity-linked returns) as the in-sample period. They observe that tail risk measures significantly vary across the various models. This stresses the importance of carefully selecting the model when hedging investment guarantees. Given that the Canadian Institute of Actuaries recommends the use of stochastic models for reserving future losses on ELPs, it is important to have a measure that can serve as a yardstick to both insurers and regulators in comparing various models, hence the consideration for robust approaches to evaluate ELPs. I propose to derive hedging strategies under worst-case scenarios and robust control approaches. Both concepts are robust adaptations of risk-control strategies introduced by Gaillardetz & Hachem (2019). Osei Mireku* (2019) investigates the robust counterpart hedging strategy when the CVaR is used in the constraint. He presents approximate solutions by sampling different uncertainty sets of probability mass functions. I intend to investigate other approaches (e.g. numerical methods) since simulation results are not consistent. Zhu & Fukushima (2009) apply the concept of worst-case local CVaR in portfolio management. Gaillardetz & Hachem (2019) show that hedging strategies obtained by minimizing the local CVaR are outperformed by strategies based on the coherent dynamic risk measure, which minimizes the local CVaR while penalizing the future losses. I propose to apply the results from Zhu & Fukushima (2009) and derive the worst-case coherent dynamic risk measure. I propose to investigate robust hedging strategies, where the risk measures are replaced by non-stochastic measurements in the risk-control strategies. These generalize the expensive super-replicating strategy in which no positive loss is allowed. The non-stochastic measurements may concede some positive losses, but restrain them by imposing constraints. Based on the results of Ben-Tal et al. (2009), computationally tractable equivalent reformulations can be used to relax the discrete assumption in the underlying financial process. The relaxation assumes a bounded continuous financial process, which is usually constrained using some upper and lower bounds. In this case, the solutions can be represented by the convex combination of the extremes.