Abstract
The paper investigates multivariate extensions of the Rothschild-Stiglitz notions and of a stronger notion of increasing univariate risk for arbitrarily distributed multivariate prospects with equal as well as unequal mean vectors. In addition, two multivariate versions of increasing variance are considered. The relations between the multivariate notions correspond very closely to known relations between the univariate ones. For multinormal prospects, a multivariate mean-variance rule is stated which is equivalent to preference in terms of expected concave (resp. convex) utility.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gaffke, N. and Krafft, O. (1982): Matrix Inequalities in the Löwner Ordering, in B. Körte ed.: Modern Applied Mathematics. Optimization and Operations Research, Amsterdam (North Holland)
Goovaerts, M.J., De Vylder, F., and Haezendonk, J. (1982): Ordering of Risks: A Review, Insurance: Mathematics and Economics 1 131–163
Gould, J.P. (1974): Risk, Stochastic Preference, and the Value of Information, J. Econ. Theory 8, 64–84
Kihlstrom, R.E. and Mirman, L.J. (1981): Constant, Increasing and Decreasing Risk Aversion with Many Commodities, Review Economic Studies 48, 271–280
Levhari, D., Paroush, J, and Peleg, B. (1975): Efficiency Analysis for Multivariate Distributions, Review Economic Studies 42, 87–91
Levy, H. (1980) ed.: Research in Finance 2, New York (Academic Press)
Mosler, K.C. (1982): Entscheidungsregeln bei Risiko: Multivariate stochastisehe Dominanz, Berlin u.a. (Springer)
Mosler, K.C. (1983): Characterization of Some Stochastic Orderings in Multinormal and Related Distributions, in: H. Steckhan et al. eds.: Operations Research Proceedings 1983, New York u.a. (Springer)
Rothschild, M. and Stiglitz, J.E. (1970): Increasing Risk: I. A Definition, J. Econ. Theory 2, 225–243
Rothschild, M. and Stiglitz, J.E. (1971): Increasing Risk: II. Its Economic Consequences, J. Econ. Theory 3, 66–84
Rüschendorf, L. (1981): Ordering of Distributions and Rearrangement of Functions, Annals of Probab. 9, 276–283
Strassen, V. (1965): The Existence of Probability Measures with Given Marginals, Ann. of Math. Statist. 36, 423–439
Whitmore, G.A. and Findlay, M.C. (1978) eds.: Stochastic Dominance: An Approach to Decision Making Under Risk, Lexington, Mass. (D.C. Heath)
Wilks, S. (1962): Mathematical Statistics, New York (J. Wiley)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mosler, K.C. (1984). Increasing Multivariate Risk: Some Definitions. In: Bamberg, G., Spremann, K. (eds) Risk and Capital. Lecture Notes in Economics and Mathematical Systems, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45569-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-45569-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12923-3
Online ISBN: 978-3-642-45569-8
eBook Packages: Springer Book Archive