Abstract
In financial optimization, the future distribution of wealth is projected by methods of statistical estimation and simulation. For making decisions, different wealth distributions have to be compared and the optimal has to be chosen. In this paper we discuss methods of assignining measures for risk (which are to be minimized) and measures for safety (which are to be maximized) to wealth distributions. Some properties of the presented measures are shown.
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References
Arrow K.J. (1971): Essays in the theory of risk-bearing. Markham, Chicago
Artzner Ph., Delbaen F., Eber J.-M., Heath D. (1998): Coherent measures of risk. Preprint
Ferschl F. (1985): Deskripive Statistik. Physica Verlag (in German)
Fishburn P.C. (1980): Stochastic Dominance and Moments of Distributions. Mathematics of Operations Research 5, 94 — 100
Huang C.-F., Litzenberger R. (1988): Foundations of Financial Economics, Prentice Hall, Englewood Cliffs, New Jersey
Jia Jianmin, Dyer J. (1996): A Standard Measure of Risk and Risk-value Models. Management Science 42, (12), 1691 — 1705
Konno H., Yamazaki H. (1991): Mean Absolute Deviation Portfolio Optimization Model and its Applications to Tokyo Stock Market. Management Science 37, 519 — 531
Markowitz, H.M. (1952): Portfolio selection. Journal of Finance 7, 77–91
Ogryczak W. (1998): Stochastic dominance relation and linear risk measures. 23rd Meeting of the EURO Working group on Financial Modelling, Cracow, Poland
Pflug G. Ch. (1998): Risk reshaping contracts and stochastic optimization. Central European Journal of Operations Research and Economics 5, (3–4), 205 — 230
Pratt J. (1964): Risk aversion in the small and in the large. Econometrics 32, 122 — 136
Rao R.R., Ren Z.D. (1991): Theory of Orlicz spaces. Marcel Dekker, New York
Rejda, George E. (1992): Principles of Risk Management and Insurance. Harper Collins, New York
Ritchie Bob (1993): Business risk management. Chapman and Hall, London
Ruszcynski A., Ogryczak W. (1997): From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures. IR-97–027, IIASA, Laxenburg, Austria
Yaari, Menhem E. (1986):. Univariate and multivariate comparisons of risk aversion: a new approach. Essays in honor of Kenneth J. Arrow, Vol. III. ( W. Heller, R. Starr, D. Starrett eds.). Cambridge University Press
Yitzhaki S. (1982): Stochastic Dominance, Mean Variance and Gini’s Mean Difference. The American Economic Review 72, 178 — 185
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© 1999 Springer-Verlag Berlin Heidelberg
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Pflug, G.C. (1999). How to Measure Risk?. In: Leopold-Wildburger, U., Feichtinger, G., Kistner, KP. (eds) Modelling and Decisions in Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12519-9_3
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DOI: https://doi.org/10.1007/978-3-662-12519-9_3
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2462-9
Online ISBN: 978-3-662-12519-9
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