A note on P- vs. Q-expected loss portfolio constraints
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A note on P- vs. Q-expected loss portfolio constraints. / Gu, Jia Wen; Steffensen, Mogens; Zheng, Harry.
In: Quantitative Finance, Vol. 21, No. 2, 2021, p. 263-270.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A note on P- vs. Q-expected loss portfolio constraints
AU - Gu, Jia Wen
AU - Steffensen, Mogens
AU - Zheng, Harry
PY - 2021
Y1 - 2021
N2 - We consider portfolio optimization problems with expected loss constraints under the physical measure (Formula presented.) and the risk neutral measure (Formula presented.), respectively. Using Merton's portfolio as a benchmark portfolio, the optimal terminal wealth of the (Formula presented.) -risk constraint problem can be easily replicated with the standard delta hedging strategy. Motivated by this, we consider the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint and compare its solution with the true optimal solution of the (Formula presented.) -risk constraint problem. We show the existence and uniqueness of the optimal solution to the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint, and provide a tractable evaluation method. The (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint is not only easier to implement with standard forwards and puts on a benchmark portfolio than the (Formula presented.) -risk constraint problem, but also easier to solve than either of the (Formula presented.) - or (Formula presented.) -risk constraint problem. The numerical test shows that the difference of the values of the two strategies (the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint and the optimal strategy solving the (Formula presented.) -risk constraint problem) is reasonably small.
AB - We consider portfolio optimization problems with expected loss constraints under the physical measure (Formula presented.) and the risk neutral measure (Formula presented.), respectively. Using Merton's portfolio as a benchmark portfolio, the optimal terminal wealth of the (Formula presented.) -risk constraint problem can be easily replicated with the standard delta hedging strategy. Motivated by this, we consider the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint and compare its solution with the true optimal solution of the (Formula presented.) -risk constraint problem. We show the existence and uniqueness of the optimal solution to the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint, and provide a tractable evaluation method. The (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint is not only easier to implement with standard forwards and puts on a benchmark portfolio than the (Formula presented.) -risk constraint problem, but also easier to solve than either of the (Formula presented.) - or (Formula presented.) -risk constraint problem. The numerical test shows that the difference of the values of the two strategies (the (Formula presented.) -strategy fulfilling the (Formula presented.) -risk constraint and the optimal strategy solving the (Formula presented.) -risk constraint problem) is reasonably small.
KW - -strategy fulfilling -risk constraint
KW - Expected loss constraint
KW - Optimal Portfolio
KW - Physical measure
KW - Risk-neutral measure
UR - http://www.scopus.com/inward/record.url?scp=85088833498&partnerID=8YFLogxK
U2 - 10.1080/14697688.2020.1764086
DO - 10.1080/14697688.2020.1764086
M3 - Journal article
AN - SCOPUS:85088833498
VL - 21
SP - 263
EP - 270
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
IS - 2
ER -
ID: 249305114