Robust Optimizations For Equity-Linked Products

本提案的主要目标是为股票关联产品（elp）制定稳健的对冲策略。elp是一种保险产品，提供有限的股票指数（股票指数年金）或共同基金（可变年金）的表现，同时提供预定的保证金额。elp被认为是一种长期金融衍生品，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，并对这些模型进行了样本外分析，使用金融危机（以及相关的观察到的与股票相关的回报）作为样本内期。他们观察到，尾部风险的度量在不同的模型中存在显著差异。这就强调了在对冲投资担保时谨慎选择模型的重要性。鉴于加拿大精算师协会建议使用随机模型来保留elp的未来损失，因此在比较各种模型时，有一种可以作为保险公司和监管机构衡量标准的措施是很重要的，因此需要考虑采用稳健的方法来评估elp。

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.