Formulate the allocator utility function U_a^i

Develop an explicit functional specification for the allocator utility function U_a^i: R^k -> R used by capital allocator a to evaluate the realised k-dimensional performance vector of a strategy within OpenAlpha’s capital allocation optimization, ensuring consistency with the stated assumptions of monotonicity in beneficial directions and concavity to reflect risk aversion.

Background

In the OpenAlpha framework, each allocator evaluates a strategy via a utility function U_a^i that maps a multi-dimensional metric vector (e.g., return, volatility, drawdown, liquidity impact) to a scalar utility. This utility directly shapes expected utility terms in the capital allocation optimization.

The paper specifies qualitative properties for U_a^i (monotonicity in beneficial directions and concavity for risk aversion) but does not commit to a particular functional form, leaving the exact specification open for future work.