Lévy processes in actuarial ruin theory and exotic option pricing

最近由各国违约引发的金融市场动荡，让人们重新认识到风险衡量对于维持充足的资本金要求和有效定价金融产品的重要性。大多数工业化国家已经制定了执行程序以识别、衡量和分析风险的综合框架。 精算破产理论旨在对保险公司的财富进行建模，并衡量其风险。同样，信用风险中的结构性模型对企业和金融机构的偿付能力也很感兴趣。另一方面，实践者和学者已经认识到，简单的金融资产价格随机模型不能解释市场上观察到的经验事实。与此同时，写在这些资产上的金融衍生品的复杂性也在不断增加。在所有情况下，都需要复杂的金融模型和强大的数学技术，设计用于风险衡量以及金融工具的定价和对冲。 这项研究的重点是概率和随机过程之间的相互作用，与精算学和金融学。精算学和金融学中出现的问题催生了概率论和随机过程理论的创新研究。另一方面，分析精算师和投资银行家的兴趣模型，需要对基础模型中使用的数学有很好的了解。预计将开发新的分析和概率数学技术来执行上述分析。

The recent turmoil in financial markets, triggered by defaults in various countries, has shed new lights on the importance of risk measurement for maintaining adequate capital requirements and efficiently pricing financial products. A comprehensive framework for implementing procedures to identify, measure, and analyze risk has been developed in most industrialized countries. Actuarial ruin theory aims at modelling, and measuring the risk of, the wealth of an insurance company. Very similarly, structural models in credit risk are interested in the solvency of firms and financial institutions. On the other hand, it has been acknowledged by practitioners and academics that simple stochastic models for the price of financial assets can not explain empirical facts observed on the markets. At the same time, the complexity of financial derivatives written on those assets is constantly increasing. In all cases, there is a need for sophisticated financial models and powerful mathematical techniques designed for risk measurement and for the pricing and hedging of financial instruments. This research program focuses on the interactions between probability and stochastic processes, with actuarial science and finance. Problems arising in actuarial science and finance generate innovative research in the theory of probability and stochastic processes. On the other hand, the analysis of models of interest for actuaries and investment bankers requires a good knowledge of the mathematics used in the underlying model. It is expected that new analytic and probabilistic mathematical techniques will be developed to perform the analyses alluded to above.