Collateral once again

Behavioral arbitrage with collateral and uncertain deliveries

“…That is for each agent h ∈ H , d h j (s) = min{ p s R j (s), p s Y (s)C j }ϕ h j . Then, γ s = 1, hence K j (s) = min{ p s R j (s), p s Y (s)C j } for all j, s. In that case, we obtain the results obtained by Fajardo (2005) and Orrillo (2005). Since, in that case there would not be uncertainty in relation to deliveries, then no need for averages, that is the absence of BAO would imply the absence of PAO.…”

“…That is for each agent h ∈ H , d h jl (s) = min{R jl (s), Y l (s)C jl }ϕ h j . Then, if we consider an anonymous market with rational agents γ s = 1, hence K jl (s) = min{R jl (s), Y l (s)C jl } for all j, s, l. In that case, we can not obtain the results obtained by Fajardo (2005) and Orrillo (2005). Since, we can not guarantee l p s,l K jl (s) = min{ p s R j (s), p s Y (s)C j } -Also, when λ h ≡ 0, we can not obtain the results in Fajardo and Lacerda (2008), since the absence of our GBAO (implies absence of PAO) do not imply the absence of the statistical arbitrage opportunities considered by them.…”

“…Proof Here we follow the ideas of Orrillo (2005). That is, it is enough to prove that the budget set is bounded.…”

“…In the exogenous collateral context we have the results of Fajardo (2005) and Orrillo (2005), that can be derived from the arbitrage definition introduced by Araújo et al (2005). When utility penalties are present, Fajardo (2009) try to address the absence of pure arbitrage opportunities implications, using a not very suitable arbitrage definition.…”

Existence of collateral Equilibrium without survival assumption

“…Under (A1) the investor's problem has a solution if, and only if, there are no arbitrage opportunities, see Orrillo (2005). That is, if and only if the following condition is satisfied:…”