Natural hedging in continuous time life insurance

IF 0.8 Q4 BUSINESS, FINANCE

European Actuarial Journal Pub Date : 2023-01-09 DOI:10.2139/ssrn.4086893

Anna Kamille Nyegaard

引用次数: 0

Abstract

Life insurance companies face several types of risks including financial risks and insurance risks. Financial risks can to a large extent be hedged by trading in the financial market, but there exists no such market for insurance risks. We suggest an alternative to hedge insurance risks. In a multi-state setup in continuous time life insurance, we describe the concept of natural hedging, which enables us to compose a portfolio of different insurance products where the liabilities are unaffected by shifts in the transition intensities. We describe how to find and how to calculate the natural hedging strategy using directional derivatives (Gateaux derivatives) to measure the sensitivity of the life insurance liabilities with respect to shifts in the transition intensities of a Markov chain governing the state of the insured. Furthermore, we implement the natural hedging strategy in two numerical examples based on the survival model and the disability model, respectively.

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连续时间人寿保险中的自然套期保值

人寿保险公司面临多种风险，包括财务风险和保险风险。金融风险在很大程度上可以通过金融市场交易来对冲，但保险风险不存在这样的市场。我们建议一种替代对冲保险风险的方法。在连续时间人寿保险的多状态设置中，我们描述了自然套期保值的概念，它使我们能够组成不同保险产品的投资组合，其中负债不受过渡强度变化的影响。我们描述了如何使用定向衍生品（Gateaux衍生品）来寻找和计算自然套期保值策略，以衡量人寿保险负债对控制被保险人状态的马尔可夫链的转移强度变化的敏感性。此外，我们分别在生存模型和残疾模型的基础上，在两个数值例子中实现了自然套期保值策略。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Actuarial Journal BUSINESS, FINANCE-

CiteScore

2.30

自引率

8.30%

发文量

期刊介绍： Actuarial science and actuarial finance deal with the study, modeling and managing of insurance and related financial risks for which stochastic models and statistical methods are available. Topics include classical actuarial mathematics such as life and non-life insurance, pension funds, reinsurance, and also more recent areas of interest such as risk management, asset-and-liability management, solvency, catastrophe modeling, systematic changes in risk parameters, longevity, etc. EAJ is designed for the promotion and development of actuarial science and actuarial finance. For this, we publish original actuarial research papers, either theoretical or applied, with innovative applications, as well as case studies on the evaluation and implementation of new mathematical methods in insurance and actuarial finance. We also welcome survey papers on topics of recent interest in the field. EAJ is the successor of six national actuarial journals, and particularly focuses on links between actuarial theory and practice. In order to serve as a platform for this exchange, we also welcome discussions (typically from practitioners, with a length of 1-3 pages) on published papers that highlight the application aspects of the discussed paper. Such discussions can also suggest modifications of the studied problem which are of particular interest to actuarial practice. Thus, they can serve as motivation for further studies.Finally, EAJ now also publishes ‘Letters’, which are short papers (up to 5 pages) that have academic and/or practical relevance and consist of e.g. an interesting idea, insight, clarification or observation of a cross-connection that deserves publication, but is shorter than a usual research article. A detailed description or proposition of a new relevant research question, short but curious mathematical results that deserve the attention of the actuarial community as well as novel applications of mathematical and actuarial concepts are equally welcome. Letter submissions will be reviewed within 6 weeks, so that they provide an opportunity to get good and pertinent ideas published quickly, while the same refereeing standards as for other submissions apply. Both academics and practitioners are encouraged to contribute to this new format. Authors are invited to submit their papers online via http://euaj.edmgr.com.