Research Article: General equilibrium with endogenous trading constraints

Date Published: September 17, 2018

Publisher: Public Library of Science

Author(s): Sebastián Cea-Echenique, Juan Pablo Torres-Martínez, Alessandro Spelta.

http://doi.org/10.1371/journal.pone.0203814

Abstract

In a competitive model where agents are subject to endogenous trading constraints, we make the access to financial trade dependent on prices and consumption decisions. Our framework is compatible with the existence of both credit market segmentation and market exclusion. In this context, we show equilibrium existence in two scenarios. In the first one, individuals can fully hedge the payments of segmented financial contracts by trading unsegmented assets. In the second one, it is assumed that agents may compensate with increments in present demand the losses of well-being generated by reductions of future consumption.

Partial Text

Equilibrium in incomplete markets where agents are subject to restricted participation was studied in seminal articles by [1], [2] and [3] or [4]. [1] guarantees equilibrium existence in real asset markets under exogenous short-sale constraints. [3] or [4] and [2] explore a more general framework in economies with nominal assets, considering restrictions given by closed and convex sets containing the zero vector.

We focus on a two-period economy with a finite set of agents and uncertainty about the realization of a state of nature at the second period. Let S={0}∪S be the set of states of nature in the economy, where s = 0 denotes the unique state at the first period and S denotes the finite set of states that can be attained at the second period.

In this section we show that our general approach to incomplete markets with trading constraints is compatible with the existence of security exchanges or assets backed by financial collateral.

When traditional fixed-point techniques are used to prove the existence of a competitive equilibrium, one of the main steps is to ensure that endogenous variables can be bounded without adding frictions on the model. Since Assumption B induces endogenous bounds on market feasible allocations, we only need to find upper bounds for asset prices.

We provide a general framework for two-period economies with uncertainty where restricted access to markets is considered. We extend the literature by allowing a general form of constraints in consumption and portfolios that we called trading constraints in the spirit of [15]. In the one hand, we include price dependence in trading contraints generalizing configurations where restrictions are exogenous to the model. In the other hand, we include frictions to investment opportunities that were not present before in the context of endogenous trading constraints.

For each M∈N, let P(M)≔P×[0,M]J∖Ju⊆P where
P={((ps)s∈S,(qj)j∈Ju)∈R+L×S×R+Ju:∥(p0,(qj)j∈Ju)∥Σ=1∧∥ps∥Σ=1,∀s∈S}.

For each agent i∈I⋄, let V˜i:R+L×S→R be the function defined by
V˜i(xi)=vl(i)i(min{x0,l(i)i,2W0,l(i)})+ρimax{x0,l(i)i-2W0,l(i),0}+vi((x0,ri)r≠l(i),(xsi)s∈S),
where l(i)∈L is the commodity that satisfies the condition of the Corollary, W0,l(i)=∑h∈Iw0,l(i)h, and ρi∈∂vl(i)i(2W0,l(i)). As customary, ∂vl(i)i(x)≔{ρ∈R:vl(i)i(y)-vl(i)i(x)≤ρ(y-x),∀y≥0} denotes the super-differential of vl(i)i at point x. Notice that, as W0≔(W0,l)l∈L≫0, the monotonicity and concavity of vl(i)i ensure that ∂vl(i)i(2W0,l(i)) is a non-empty subset of R+.

 

Source:

http://doi.org/10.1371/journal.pone.0203814