Two types of risk

Filar, JA; Kang, B

Two types of risk

Filar, JA Kang, B

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Publication Type:: Chapter
Citation:: International Series in Operations Research and Management Science, 2006, 94 pp. 109 - 140
Issue Date:: 2006-01-01

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Field	Value	Language
dc.contributor.author	Filar, JA	en_US
dc.contributor.author	Kang, B	en_US
dc.date.issued	2006-01-01	en_US
dc.identifier.citation	International Series in Operations Research and Management Science, 2006, 94 pp. 109 - 140	en_US
dc.identifier.uri	http://hdl.handle.net/10453/7817
dc.description.abstract	© 2006, Springer New York LLC . All rights reserved. The risk encountered in many environmental problems appears to exhibit special “two-sided” characteristics. For instance, in a given area and in a given period, farmers do not want to see too much or too little rainfall.They hope for rainfall that is in some given interval.We formulate and solve this problem with the help of a “two-sided loss function” that depends on the above range. Even in ﬁnancial portfolio optimization a loss and a gain are “two sides of a coin”, so it is desirable to deal with them in a manner that reﬂects an investor’s relative concern. Consequently, in this paper, we define Type I risk: “the loss is too big” and Type II risk: “the gain is too small”. Ideally, we would want to minimize the two risks simultaneously. However, this may be impossible and hence we try to balance these two kinds of risk. Namely, we tolerate certain amount of one risk when minimizing the other. The latter problem is formulated as a suitable optimization problem and illustrated with a numerical example.	en_US
dc.relation.ispartof	International Series in Operations Research and Management Science	en_US
dc.title	Two types of risk	en_US
dc.type	Chapter
utslib.citation.volume	94	en_US
utslib.for	010401 Applied Statistics	en_US
utslib.for	010302 Numerical Solution of Differential and Integral Equations	en_US
utslib.for	010205 Financial Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
utslib.copyright.status	open_access
pubs.publication-status	Published	en_US
pubs.volume	94	en_US

Abstract:

© 2006, Springer New York LLC . All rights reserved. The risk encountered in many environmental problems appears to exhibit special “two-sided” characteristics. For instance, in a given area and in a given period, farmers do not want to see too much or too little rainfall.They hope for rainfall that is in some given interval.We formulate and solve this problem with the help of a “two-sided loss function” that depends on the above range. Even in ﬁnancial portfolio optimization a loss and a gain are “two sides of a coin”, so it is desirable to deal with them in a manner that reﬂects an investor’s relative concern. Consequently, in this paper, we define Type I risk: “the loss is too big” and Type II risk: “the gain is too small”. Ideally, we would want to minimize the two risks simultaneously. However, this may be impossible and hence we try to balance these two kinds of risk. Namely, we tolerate certain amount of one risk when minimizing the other. The latter problem is formulated as a suitable optimization problem and illustrated with a numerical example.

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http://hdl.handle.net/10453/7817