Numeraire-Invariant Quadratic Hedging and Mean–Variance Portfolio Allocation
研究了无风险资产可能缺失的半鞅市场中的二次对冲问题，建立了计价单位变换前后的等价性，无需选择参考资产即可直接计算最优策略，并给出了有效前沿的简化计算方法。
The paper investigates quadratic hedging in a 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 analysis yields a streamlined computation of the efficient frontier for the pure investment problem in terms of three easily interpreted processes. The main result advances our understanding of the efficient frontier formation in the most general case in which a risk-free asset may not be present. Several illustrations of the numeraire-invariant approach are given.