Hedging derivatives: from finance to actuarial science

二十多年来，金融和保险产品的定价、套期保值和风险管理一直是研究的重点对象。尽管巨大的研究努力已经解决了重要的方面，但仍有“谜题”有待解决。本研究项目集中于金融计量经济学和精算科学文献的两个主要方面。项目的第一部分调查定价和对冲金融衍生品，特别是期权和波动衍生品。尽管绝大多数数学金融文献在连续时间内检查这些，主要是由于这种设置提供的可追溯性，但通常在固定日期采样的兴趣数量，因此，离散时间设置可能更合适。在这个项目中，我们开发了基于广义非线性时间序列模型的期权和方差掉期定价和套期保值的新方法，并通过研究相应数量的利息之间的收敛性来说明它们与连续时间限制的相互作用。我们进一步计划研究如何将这些方法应用于对冲保险产品。在提案的第二部分，我们探讨了保险公司所面临的主要挑战之一，即量化其最低所需资本和对多元化金融资产组合的最佳投资。在偿付能力指令II的激励下，我们提出了监管机构施加不同偿付能力约束的非寿险公司新的优化问题。这些优化问题将在静态和动态设置中实现。

The pricing, hedging and risk management of financial and insurance products have been key objects of study in over two decades. Although tremendous research efforts have addressed important aspects, there are still 'puzzles' yet to be solved. This research project focus on two main strands from the financial econometrics and actuarial science literature. The first part of the project investigates the pricing and hedging of financial derivatives, in particular options and volatility derivatives. Although a vast majority of the mathematical finance literature examines these in continuous time, mainly due to the tractability offered by this setup, quantities of interest are in general sampled at fixed dates and therefore, a discrete-time setting might be more appropriate. In this project we develop new methods for pricing and hedging of options and variance swaps based on a broad class of non-linear time series models and we illustrate the interplay with their continuous time limits, by studying the convergence between the corresponding quantities of interest. We further plan to investigate how these methods can be applied to hedging insurance products. In the second part of the proposal, we explore one of the major challenges faced by an insurance company regarding the quantification of its minimum required capital and its optimal investment into a well-diversified portfolio of financial assets. Motivated by the Solvency II Directives, we propose new optimization problems for non-life insurance companies, with different solvency constraints imposed by regulators. These optimization problems will be implemented in both static, and dynamic settings.