保险估值：一种两步广义回归方法
Insurance valuation: A two-step generalised regression approach
AI总结：
本文提出一种两步广义回归对冲方法，使投资组合对风险度量中性，满足偿付能力约束，并给出神经网络算法实现保险负债估值与对冲。
摘要：
当前保险中的公允价值估值方法通常采用两步法，将二次对冲与对剩余负债应用风险度量相结合，以获得资本成本边际。在这种方法中，监管风险度量所代表的偏好并未反映在对冲过程中。我们通过一种基于广义回归论证的替代性两步对冲程序来解决这一问题，该程序产生的投资组合对风险度量（如风险价值或期望损失）是中性的。首先，通过局部二次对冲确定一个旨在复制负债的可交易资产组合。其次，使用替代目标函数对剩余负债进行对冲。风险边际随后被定义为对冲剩余负债所需资本的成本。在第二步使用分位数回归的情况下，年度偿付能力约束自然得到满足；此外，该投资组合是所有满足此类约束的对冲投资组合中的风险最小化者。我们提出了一种基于向后迭代方案的神经网络算法，用于保险负债的估值和对冲。该算法相当通用且易于应用，因为它仅需要风险驱动因素的模拟路径。
英文摘要：
Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.
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