Endogenous market power

No-arbitrage, state prices and trade in thin financial markets

“…Proof: These results follow, respectively, from Theorems 1 and 2 in [12]. For the sake of simplicity and completeness, Appendix A2 specializes the proofs to the case considered here.…”

“…7 For each investor i, let M i a,a measure individual her belief of how the price of asset a changes when she expands her buy order for asset a by one share. In the competitive model, this measure is exogenously fixed at zero; here, we follow [12] in letting M i a,a be endogenously determined as part of the equilibrium concept. The A × A matrix…”

“…For simplicity of notation, given an array of I − 1 positive definite matrices, ∆, let H(∆) denote the harmonic average of the array. 12 Lemma 1. Suppose that R is nonsingular.…”

“…We apply a model of economic equilibrium, based on [12], in which individual traders recognize and estimate the impact of their trades on financial prices, and in which these effects are determined endogenously as part of the equilibrium concept. For the case in which markets allow for perfect insurance, we argue that the principle of no-arbitrage asset pricing is consistent with non-competitive behavior and extend the fundamental theorem of asset pricing to the non-competitive setting.…”

“…The work initiated by T. Negishi in [8], though interesting, either required the imposition of very strong assumptions, or gave highly complex, intractable and inapplicable models: in the Negishi's approach, traders were allowed to have subjective perceptions of the price impact, which implied a great deal of arbitrariness on the determination of equilibria, unless the subjective conjectures where exogenously restricted; later attempts to impose more structure to the definition of equilibrium endowed the model with explicit strategic games, which came at the cost of tractability. 2 In this paper, we apply a model of economic equilibrium, based on [12], in which all individual traders recognize the impact that their trades have on financial prices, and in which these effects are determined endogenously as part of the equilibrium concept. 3 This model maintains the flexible, tractable and spare structure of the competitive model, but the departure from the competitive premise implies that none of the standard positive or normative results are immediately applicable, and, in particular, the necessity of a noarbitrage condition, and the derivation of an objective probability have to be argued.…”