Oussama Belhouari, Griselda Deelstra, Pierre Devolder
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Hybrid life insurance valuation based on a new standard deviation premium principle in a stochastic interest rate framework
In a complete arbitrage-free financial market, financial products are valued with the risk-neutral measure and these products are completely hedgeable. In life insurance, the approach is different as the valuation is based on an insurance premium principle which includes a safety loading. The insurer reduces the risk by pooling a vast number of independent risks. In our framework, we suggest valuations of a class of products that are dependent on both mortality and financial risk, namely hybrid life products. The main contribution of this paper is to present a generalized standard deviation premium principle in a stochastic interest rate framework, and to integrate it in different valuation operators suggested in the literature. We illustrate our methods with a classical application, namely a Pure Endowment with profit. Several numerical results are presented, and an extensive sensitivity analysis is included.
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.
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