A note on P- vs. Q-expected loss portfolio constraints

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Title: A note on P- vs. Q-expected loss portfolio constraints
Authors: Gu, J-W
Steffensen, M
Zheng, H
Item Type: Journal Article
Abstract: We consider portfolio optimization problems with expected loss constraints un-der the physical measure P and the risk neutral measure Q, respectively. Using Merton’s portfolio as a benchmark portfolio, the optimal terminal wealth of the Q-risk constraint problem can be easily replicated with the standard delta hedg-ing strategy. Motivated by this, we consider the Q-strategy fulfilling the P-risk constraint and compare its solution with the true optimal solution of theP-riskconstraint problem. We show the existence and uniqueness of the optimal solution to theQ-strategy fulfilling theP-risk constraint, and provide a tractable evalua-tion method. The Q-strategy fulfilling the P-risk constraint is not only easier toimplement with standard forwards and puts on a benchmark portfolio than the P-risk constraint problem, but also easier to solve than either of theQ- or P-riskconstraint problem. The numerical test shows that the difference of the values ofthe two strategies (the Q-strategy fulfilling the P-risk constraint and the optimal strategy solving the P-risk constraint problem) is reasonably small.
Issue Date: 1-Feb-2021
Date of Acceptance: 24-Apr-2020
URI: http://hdl.handle.net/10044/1/79808
DOI: 10.1080/14697688.2020.1764086
ISSN: 1469-7688
Publisher: Taylor & Francis (Routledge)
Start Page: 263
End Page: 270
Journal / Book Title: Quantitative Finance
Volume: 21
Issue: 2
Copyright Statement: © 2020 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 28 Jul 2020, available online: https://www.tandfonline.com/doi/full/10.1080/14697688.2020.1764086
Keywords: Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematical Methods In Social Sciences
Optimal Portfolio
Expected loss constraint
Physical measure P
Risk-neutral measure Q
Q-strategy fulfilling P-risk constraint
01 Mathematical Sciences
14 Economics
15 Commerce, Management, Tourism and Services
Publication Status: Published
Online Publication Date: 2020-07-28
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences