Robust Optimizations For Equity-Linked Products

这项建议的主要目的，是为股票挂钩产品制订稳健的重混策略。电子退休计划是一类保险产品，提供有限参与股票指数（股票指数年金）或互惠基金（可变年金）的表现，同时提供预定的保证金额。ELP被视为长期金融衍生工具，包括死亡、退保、提款和/或累积担保。在分析这些担保背后的风险时，Augustyniak & Boudreault（2012）研究了几个计量经济学模型，并使用金融危机（以及相关的观察到的股票挂钩回报率）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，尾部风险指标在各种模型中存在显著差异。这强调了在对冲投资担保时仔细选择模型的重要性。鉴于加拿大精算师协会建议使用随机模型来为电子学习产品的未来损失做准备，因此，重要的是要有一个衡量标准，可以作为保险公司和监管机构比较各种模型的准绳，因此，要考虑采用稳健的方法来评估电子学习产品。我建议在最坏的情况下推导出套期保值策略和鲁棒控制方法。这两个概念都是对Gaillardetz & Hachem（2019）引入的风险控制策略的稳健适应。Osei Mireku*（2019）研究了在约束中使用CVaR时的稳健对应对冲策略。他提出了近似的解决方案，通过抽样不同的不确定性集的概率质量函数。由于模拟结果不一致，我打算研究其他方法（例如数值方法）。Zhu &福岛（2009）将最坏情况局部CVaR的概念应用于投资组合管理。Gaillardetz & Hachem（2019）表明，通过最小化局部CVaR获得的对冲策略优于基于相干动态风险度量的策略，该策略最小化局部CVaR，同时惩罚未来损失。笔者建议应用Zhu &福岛（2009）的结果，推导出最坏情况下的相干动态风险度量。我建议研究鲁棒套期保值策略，其中的风险措施被替换为非随机测量的风险控制策略。这些概括了昂贵的超级复制策略，其中不允许有正的损失。非随机测量可能承认一些正损失，但通过施加约束来抑制它们。基于Ben-Tal et al.（2009）的结果，可以使用计算上易于处理的等价重构来放松底层金融过程中的离散假设。松弛假设一个有界连续的金融过程，这通常是限制使用一些上限和下限。在这种情况下，解可以由极值的凸组合表示。

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.