WORKSHOP ON RISK ANALYSIS AND APPLICATIONS
24 and 25 of SEPTEMBER, 2025
Institute of Mathematics and, Statistics of the University of São Paulo, Brazil
SATELLITE WORKSHOP OF
8th BRAZILIAN CONFERENCE ON STATISTICAL MODELING IN INSURANCE AND FINANCE
WORKSHOP ON RISK ANALYSIS AND APPLICATIONS
24 and 25 of SEPTEMBER, 2025
Institute of Mathematics and, Statistics of the University of São Paulo, Brazil
SATELLITE WORKSHOP OF
8th BRAZILIAN CONFERENCE ON STATISTICAL MODELING IN INSURANCE AND FINANCE
Title: Arbitrage, Relative Firms, and Latent Asymptotics in a Relative Factor Economy
A significant number of economic equilibrium models use component variables (agents, firms, commodities), with an infinite or a continuous population domain, that are heterogeneous variables in the physical reality. Arbitrage models, and arbitrage pricing theory (APT) in particular, rely on the use of the Law of Large Numbers (LLN) with the assumption of an i.i.d. distribution in the expectation (measure) of these component variables (firms) in their sample domain, to eliminate the non-systematic risk and to derive its equilibrium result. The i.i.d. of the expectation in the “growing N to infinity” asymptotics is a non-realistic assumption considering the heterogeneous nature of these component variables, and it can lead to the rejection of the model in empirical tests. By assuming the existence of the arbitrage equilibrium, we derive the implicit underlying (non)-i.i.d. in the measure Law of Large Numbers (LLN) under which the economic equilibrium holds. We provide two algorithms to derive the implicit non-i.i.d. Law of Large Numbers (LLN): (i) latent asymptotic projection method and a (ii) economic characteristics proxy method. We define this extended APT model as the relative factor economy model where we replace the i.i.d. asymptotics by a dimension-weighted asymptotics approach. Empirical tests show that (i) the relative factor economy model remains valid in cases where traditional APT factor models are rejected, and (ii) when the economic characteristics proxy method is used, the firm size, assets under management (AM), industry concentration (HerfBE), research and development (RD), and leverage characteristics represent better the heterogeneity of the variables in the non-i.i.d. diversification of non-systematic risk.