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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2451/27010
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| Title: | Viability and Equilibrium in Securities Markets with Frictions |
| Authors: | Jouini, Elyès
Kallal, Hédi |
| Keywords: | Viability
equilibrium
absence of arbitrage
free lunch
market frictions
convex and sublinear pricing ruler
consistent bid-ask prices
arbitrage bounds
equilibrium bounds |
| Issue Date: | Mar-1999 |
| Series/Report no.: | FIN-99-036 |
| Abstract: | In this paper we study some foundational issues in the theory of asset
pricing with market frictions. We model market frictions by letting the
set of marketed contingent claims (the opportunity set) be a convex set,
and the pricing rule at which these claims are available be convex. This
is the reduced form of multiperiod securities price models incorporating
a large class of market frictions. It is said to be viable as a model of
economic equilibrium if there exist price-taking maximizing agents who
are happy with their initial endowment, given the opportunity set, and
hence for whom supply equals demand. This is equivalent to the existence
of a positive linear pricing rule on the entire space of contingent
claims - an underlying frictionless linear pricing rule - that lies
below the convex pricing rule on the set of marketed claims. This is
also equivalent to the absence of asymptotic free lunches - a
generalization of opportunities of arbitrage. When a market for a non
marketed contingent claim opens, a bid-ask price pair for this claim is
said to be consistent if it is a bid-ask price pair in at least a viable
economy with this extended opportunity set. If the set of marketed
contingent claims is a convex cone and the pricing rule is convex and
sublinear, we show that the set of consistent prices of a claim is a
closed interval and is equal (up to its boundary) to the set of its
prices for all the underlying frictionless pricing rules. We also show
that there exists a unique extended consistent sublinear pricing rule -
the supremum of the underlying frictionless linear pricing rules - for
which the original equilibrium does not collapse, when a new market
opens, regardless of preferences and endowments. If the opportunity set
is the reduced form of a multiperiod securities market model, we study
the closedness of the interval of prices of a contingent claim for the
underlying frictionless pricing rules. |
| URI: | http://hdl.handle.net/2451/27010 |
| Appears in Collections: | Finance Working Papers
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