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Mathematics
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Mathematics
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Mathematics
Article . 2021
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https://dx.doi.org/10.48550/ar...
Article . 2018
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Mortality/Longevity Risk-Minimization with or without Securitization

Authors: Tahir Choulli; Catherine Daveloose; Michèle Vanmaele;

Mortality/Longevity Risk-Minimization with or without Securitization

Abstract

This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model and the time of death is arbitrary general, and hence leads to the case of a market model where there are two levels of information—the public information, which is generated by the financial assets, and a larger flow of information that contains additional knowledge about the death time of an insured. By enlarging the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction. Our key tool lies in our optional martingale representation, which states that any martingale in the large filtration stopped at the death time can be decomposed into precise orthogonal local martingales. This allows us to derive the dynamics of the value processes of the mortality/longevity securities used for the securitization, and to decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. The first main contribution of this paper resides in quantifying, as explicitly as possible, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. Our second main contribution consists of finding risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives such as longevity bonds. This generalizes the existing literature on risk-minimization using mortality securitization in many directions.

Country
Belgium
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Keywords

DECOMPOSITION, optional martingale representation, VALUATION, LIFE-INSURANCE LIABILITIES, CAPITAL-MARKETS, insurance securitization, progressively enlarged, progressively enlarged filtration, FOS: Economics and business, longevity, risk-minimization, risk decomposition, QA1-939, risk, filtration, mortality/longevity risk, time of death/random horizon/default, MERGING ACTUARIAL JUDGMENT, DEATH, unit-linked mortality contracts, mortality, Mathematical Finance (q-fin.MF), LONGEVITY RISK, Mathematics and Statistics, BONDS, Quantitative Finance - Mathematical Finance, random horizon, default, time of death, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
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gold
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