TY - JOUR
T1 - Inverse portfolio problem with coherent risk measures
AU - Grechuk, Bogdan
AU - Zabarankin, Michael
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean-deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor's preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor's coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari's dual utility. It is solved in single-period and multi-period formulations and is demonstrated in a case study with the FTSE 100 index.
AB - In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean-deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor's preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor's coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari's dual utility. It is solved in single-period and multi-period formulations and is demonstrated in a case study with the FTSE 100 index.
KW - Coherent risk measure
KW - Decision making under risk
KW - Inverse portfolio problem
KW - Portfolio optimization
UR - http://www.scopus.com/inward/record.url?scp=84952975186&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84952975186&partnerID=8YFLogxK
U2 - 10.1016/j.ejor.2015.09.050
DO - 10.1016/j.ejor.2015.09.050
M3 - Article
AN - SCOPUS:84952975186
SN - 0377-2217
VL - 249
SP - 740
EP - 750
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -