Numeraire-Invariant Quadratic Hedging and Mean-Variance Portfolio Allocation
arXiv preprint 2110.09416
35 Pages Posted: 19 Oct 2021
Date Written: October 18, 2021
The paper investigates quadratic hedging in a general semimartingale market that does not necessarily contain a risk-free asset. An equivalence result for hedging with and without numeraire change is established. This permits direct computation of the optimal strategy without choosing a reference asset and/or performing a numeraire change. New explicit expressions for optimal strategies are obtained, featuring the use of oblique projections that provide unified treatment of the case with and without a risk-free asset. The main result advances our understanding of the efficient frontier formation in the most general case where a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.
Keywords: mean-variance portfolio selection, quadratic hedging, numeraire change, oblique projection, opportunity-neutral measure
JEL Classification: G11, G12, C61
Suggested Citation: Suggested Citation