Incorporating benchmark-neutral risk-minimization into regulatory capital requirements with multiple numeraires

Determine the most suitable approach for incorporating benchmark-neutral risk-minimization into optimized regulatory capital requirements by appropriately considering multiple numeraires (including the stock growth optimal portfolio S* and the savings account S0) in the design of an institution’s capital requirement, and specify how these numeraires should be used to set critical capitalization levels and capital cost provisions in a manner consistent with asset–liability management and regulatory constraints.

Background

The paper develops benchmark-neutral (BN) pricing and risk-minimization using the stock growth optimal portfolio (GOP) S* as numeraire under an equivalent BN measure Q*. It argues BN pricing yields minimal possible prices and effectively avoids insurance–finance arbitrages of the first kind, while practical regulation often uses the savings account S0 as numeraire.

In the discussion of regulatory practice, the authors note that current frameworks rarely employ a proxy of the stock GOP as numeraire and typically rely on S0. They suggest that an optimized regulatory capital requirement may need to consider several numeraires to be most suitable, but they do not specify how to implement this integration of BN risk-minimization within regulatory capital design.

This open question targets the methodological and regulatory synthesis: how to combine BN risk-minimization with existing capital requirement regimes, including defining critical capitalization levels and capital cost provisions when multiple numeraires are appropriately considered.