State Tameness: A New Approach for Credit Constrains
Jaime A. Londono, Universidad EAFIT
Abstract
We propose a new definition for tameness within the
model of security prices as Itô processes that is
risk-aware. We give a new definition for arbitrage and
characterize it. We then prove a theorem that can be seen as an
extension of the second fundamental theorem of asset pricing, and a
theorem for valuation of contingent claims of the American type. The
valuation of European contingent claims and American contingent claims
that we obtain does not require the full range of the volatility
matrix. The technique used to prove the theorem on valuation of
American contingent claims does not depend on the Doob-Meyer
decomposition of super-martingales; its proof is constructive and
suggest and alternative way to find approximations of stopping times
that are close to optimal.
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