Stable linear-time optimisation in arbitrage pricing theory models

Gordon Ritter proposes a stable mean-variance optimisation for APT models



1 Markowitz optimisation and arbitrage pricing theory 1.1 Arbitrage pricing theory.

Many models for asset returns in empirical finance, following Ross (1976), assume a linear functional form:

  Rt+1=Xt⁢ft+ϵt,?⁢[ϵ]=0,?⁢[ϵ]=D   (1)

where Rt+1 is an n-dimensional random vector containing the cross-section of returns in excess of the risk-free rate over some time interval [t,t+1], Xt is a (non-random) n×p matrix that is known before time t, and ϵt is assumed to follow

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