Formal verification study demonstrates the logical structure of stochastic portfolio theory in mathematical finance, highlighting boundaries between proved theorems and empirical assumptions.
Stochastic Portfolio Theory provides a model-free framework in which functionally generated portfolios track the market index up to two terms: a boundary term in the generating function and the time-integral of an excess growth rate. We formalize the logical skeleton of this framework in a proof kernel and report, with deliberate precision, which parts are derived and which are assumed. Three tiers result. (i) The elementary algebra of diversification — that a component-weighted average variance dominates the corresponding diagonal basket variance — is derived from first principles as a sum-of-squares certificate, generalized term-by-term beyond the two-asset case; with full correlation, the excess growth of an arbitrary portfolio is a non-negatively weighted sum of pairwise return-difference variances, γ^{}_π = 12∑_{i
No takes yet. Share an insight, caveat, or question.
Tamás Nagy (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: