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On the (in-)dependence between financial and actuarial risks. (English) Zbl 1284.91226

Summary: Probability statements about future evolutions of financial and actuarial risks are expressed in terms of the ‘real-world’ probability measure \(\mathbb P\), whereas in an arbitrage-free environment, the prices of these traded risks can be expressed in terms of an equivalent martingale measure \(\mathbb Q\). The assumption of independence between financial and actuarial risks in the real world may be quite reasonable in many situations. Making such an independence assumption in the pricing world however, may be convenient but hard to understand from an intuitive point of view. In this pedagogical paper, we investigate the conditions under which it is possible (or not) to transfer the independence assumption from \(\mathbb P\) to \(\mathbb Q\). In particular, we show that an independence relation that is observed in the \(\mathbb P\)-world can often not be maintained in the \(\mathbb Q\)-world.

MSC:

91B30 Risk theory, insurance (MSC2010)
91G99 Actuarial science and mathematical finance
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[1] Delbaen, F.; Schachermayer, W., The mathematics of arbitrage, 373, (2008), Springer · Zbl 1106.91031
[2] Denuit, M.; Dhaene, J.; Goovaerts, M. J.; Kaas, R., Actuarial theory for dependent risks: measures, orders and models, (2005), Wiley
[3] Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., The concept of comonotonicity in actuarial science and finance: theory, Insurance: Mathematics & Economics, 31, 1, 3-33, (2002) · Zbl 1051.62107
[4] Dhaene, J.; Denuit, M.; Goovaerts, M. J.; Kaas, R.; Vyncke, D., The concept of comonotonicity in actuarial science and finance: applications, Insurance: Mathematics & Economics, 31, 2, 133-161, (2002) · Zbl 1037.62107
[5] Dhaene, J., Kukush, A., Linders, D., 2013. The multivariate Black & Scholes market: conditions for completeness and no-arbitrage, Theory of Probability and Mathematical Statistics (in press). · Zbl 1304.91215
[6] Gorvett, R. W., Insurance securitization: the development of a new asset class, Casualty Actuarial Society, 133-172, (1999)
[7] Jalen, L.; Mamon, R., Valuation of contingent claims with mortality and interest rate risks, Mathematical and Computer Modelling, 49, 9-10, 1893-1904, (2009) · Zbl 1171.91349
[8] Shiryaev, A. N.; Kabanov, Y. M.; Kramkov, O. D.; Melnikov, A. V., Towards the theory of pricing of options of both European and American types. I. discrete time, Theory of Probability and its Applications, 39, 1, 23-79, (1994) · Zbl 0833.60064
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