On cross-risk vulnerability. (English) Zbl 1231.91215
Summary: We introduce the notion of cross-risk vulnerability to generalize the concept of risk vulnerability introduced by C. Gollier and J. W. Pratt [Econometrica 64, No. 5, 1109–1123 (1996; Zbl 0856.90014)]. While risk vulnerability captures the idea that the presence of an unfair financial background risk should make risk-averse individuals behave in a more risk-averse way with respect to an independent financial risk, cross-risk vulnerability extends this idea to the impact of a non-financial background risk on the financial risk. It provides an answer to the question of the impact of a background risk on the optimal coinsurance rate and on the optimal deductible level. We derive necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also analyze the question of the sub-additivity of risk premia and show to what extent cross-risk vulnerability provides an answer.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 91B16 | Utility theory |
Citations:
Zbl 0856.90014References:
| [1] | Bleichrodt, H.; Crainich, D.; Eeckhoudt, L., Comorbidities and the willingness to pay for health improvements, Journal of Public Economics, 87, 2399-2406 (2003) |
| [2] | Bleichrodt, H.; Eeckhoudt, L., Survival risks, intertemporal consumption, and insurance: The case of distorted probabilities, Insurance: Mathematics and Economics, 38, 335-346 (2006) · Zbl 1132.91016 |
| [3] | Chalfant, J. A.; Finkelshtain, I., Portfolio choices in the presence of other risk, Management Science, 39, 925-936 (1993) · Zbl 0785.90010 |
| [4] | Chiu, W. H., Degree of downside risk aversion and self-protection, Insurance: Mathematics and Economics, 36, 93-101 (2005) · Zbl 1111.91022 |
| [5] | Courbage, C., On bivariate risk premia, Theory and Decision, 50, 29-34 (2001) · Zbl 0980.91043 |
| [6] | Doherty, N.; Schlesinger, H., Optimal insurance in incomplete markets, Journal of Political Economy, 91, 1045-1054 (1983) |
| [7] | Doherty, N.; Schlesinger, H., The optimal deductible for an insurance policy when initial wealth is random, Journal of Business, 56, 555-565 (1983) |
| [8] | Doherty, N.; Schlesinger, H., A note on risk premiums with random initial wealth, Insurance: Mathematics and Economics, 5, 183-185 (1986) |
| [9] | Eeckhoudt, L.; Kimball, M., Background risk, Prudence, and the demand for insurance, (Contributions to Insurance Economics (1992), Kluwer Academic Publishers), 239-254 |
| [10] | Eeckhoudt, L.; Gollier, C., Which shape for the cost curve of risk?, The Journal of Risk and Insurance, 68, 387-402 (2001) |
| [11] | Eeckhoudt, L.; Gollier, C.; Schlesinger, H., Changes in background risk taking behavior, Econometrica, 64, 683-689 (1996) · Zbl 0849.90002 |
| [12] | Eeckhoudt, L.; Gollier, C.; Schlesinger, H., Economic and Financial Decisions under Risk (2005), Princeton University Press |
| [13] | Eeckhoudt, L.; Rey, B.; Schlesinger, H., A good sign for multivariate risk taking, Management Science, 53, 117-124 (2007) |
| [14] | Eeckhoudt, L.; Schlesinger, H., Putting risk in its proper place, American Economic Review, 96, 280-289 (2006) |
| [15] | Eichner, T., Mean variance vulnerability, Management Science, 54, 586-593 (2008) |
| [16] | Eichner, T.; Wagener, A., Variance vulnerability, background risks, and mean-variance preferences, The Geneva Papers on Risk and Insurance Theory, 28, 173-184 (2003) |
| [17] | Epstein, L. G.; Tanny, S. M., Increasing generalized correlation: A definition and some economic consequences, Canadian Journal of Economics, 13, 16-34 (1980) |
| [18] | Evans, W. N.; Viscusi, W. K., Estimation of state-dependent utility functions using survey data, Review of Economics and Statistics, 73, 94-104 (1991) |
| [19] | Franke, G.; Schlesinger, H.; Stapleton, R. C., Multiplicative background risk, Management Science, 52, 146-153 (2006) · Zbl 1232.91347 |
| [20] | Franke, G., Stapleton, R.C., Subrahmanyam, M.G, 2005. Incremental risk vulnerability. Working paper; Franke, G., Stapleton, R.C., Subrahmanyam, M.G, 2005. Incremental risk vulnerability. Working paper |
| [21] | Gollier, G., The Economics of Risk and Time (2001), MIT Press: MIT Press Cambridge, MA · Zbl 0991.91001 |
| [22] | Gollier, C.; Pratt, J. W., Risk vulnerability and the tempering effect of background risk, Econometrica, 64, 1109-1124 (1996) · Zbl 0856.90014 |
| [23] | Hotelling, H., Relations between two sets of variates, Biometrika, 28, 321-377 (1936) · Zbl 0015.40705 |
| [24] | Kihlstrom, R.; Romer, D.; William, S., Risk aversion with random initial wealth, Econometrica, 49, 911-920 (1981) · Zbl 0461.90018 |
| [25] | Kimball, M. S., Standard risk aversion, Econometrica, 61, 589-611 (1993) · Zbl 0771.90017 |
| [26] | Kischka, P., Aspects of optimal insurance demand when there are uninsurable risks, Insurance: Mathematics and Economics, 7, 9-14 (1988) · Zbl 0651.62099 |
| [27] | Menegatti, M., On the conditions for precautionary savings, Journal of Economic Theory, 98, 189-193 (2001) · Zbl 1028.91568 |
| [28] | Nachman, D. C., Preservation of more risk averse under expectations, Journal of Economic Theory, 28, 361-368 (1982) · Zbl 0498.90006 |
| [29] | Pratt, J. W., Risk aversion in the small and the large, Econometrica, 32, 122-136 (1964) · Zbl 0132.13906 |
| [30] | Pratt, J. W.; Zeckhauser, R. J., Proper risk aversion, Econometrica, 55, 143-154 (1987) · Zbl 0612.90006 |
| [31] | Quiggin, J., Background risk in generalized expected utility theory, Economic Theory, 22, 607-611 (2003) · Zbl 1044.91023 |
| [32] | Quiggin, J.; Chambers, R. G., Risk premiums and benefit measures for generalized expected utility theories, Journal of Risk and Uncertainty, 17, 121-137 (1998) · Zbl 0917.90021 |
| [33] | Rey, B., Total and partial bivariate risk premia, Theory and Decision, 55, 59-69 (2003) · Zbl 1073.91045 |
| [34] | Richard, S., Multivariate risk aversion, utility independence and separable utility functions, Management Science, 22, 12-21 (1975) · Zbl 0317.90008 |
| [35] | Schlesinger, H., The optimal level of deductibility in insurance contracts, Journal of Risk and Insurance, 48, 465-481 (1981) |
| [36] | Safra, Z.; Segal, U., Constant risk aversion, Journal of Economic Theory, 83, 19-42 (1998) · Zbl 0913.90068 |
| [37] | Sloan, F. A.; Viscusi, W. K.; Chesson, H. W.; Conover, C. J.; Whetten-Goldstein, K., Alternatives approaches to valuing intangible health losses: the evidence of multiple sclerosis, Journal of Health Economics, 17, 475-482 (1998) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
