A note on P- vs. Q-expected loss portfolio constraints
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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.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Quantitative Finance |
Vol/bind | 21 |
Udgave nummer | 2 |
Sider (fra-til) | 263-270 |
ISSN | 1469-7688 |
DOI | |
Status | Udgivet - 2021 |
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