TY - JOUR
T1 - Optimal Portfolio Selection with VaR and Portfolio Insurance Constraints under Rank-dependent Expected Utility Theory
AU - Mi, Hui
AU - Xu, Zuo Quan
N1 - Funding Information:
The author acknowledges financial support from NSFC (No. 61304065) and Nanjing Normal University.The author acknowledges financial support from NSFC (No. 11971409), The Hong Kong RGC (GRF 15202421 and 15204622), The PolyU-SDU Joint Research Center on Financial Mathematics, The CAS AMSS-PolyU Joint Laboratory of Applied Mathematics, and The Hong Kong Polytechnic University Research Centre for Quantitative Finance (1-CE03).
Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/5
Y1 - 2023/5
N2 - This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. The martingale method, quantile formulation, and relaxation method are used to obtain explicit optimal solutions. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.
AB - This paper investigates two optimal portfolio selection problems for a rank-dependent utility investor who needs to manage his risk exposure: one with a single Value-at-Risk (VaR) constraint and the other with joint VaR and portfolio insurance constraints. The two models generalize existing models under expected utility theory and behavioral theory. The martingale method, quantile formulation, and relaxation method are used to obtain explicit optimal solutions. We have specifically identified an equivalent condition under which the VaR constraint is effective. A numerical analysis is carried out to demonstrate theoretical results, and additional financial insights are presented. We find that, in bad market states, the risk of the optimal investment outcome is reduced when compared to existing models without or with one constraint.
KW - Portfolio optimization
KW - Quantile formulation
KW - Rank-dependent expected utility
KW - Relaxation method
KW - VaR constraint
UR - http://www.scopus.com/inward/record.url?scp=85150452901&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2023.02.004
DO - 10.1016/j.insmatheco.2023.02.004
M3 - Journal article
AN - SCOPUS:85150452901
SN - 0167-6687
VL - 110
SP - 82
EP - 105
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
ER -