Martingale selection problem and asset pricing in finite discrete time
Dmitry B. Rokhlin, Rostov State University
Abstract
Given a set-valued stochastic process (Vt)t=0,...,T, we say
that the martingale selection problem is solvable if there exists an
adapted sequence of selectors ξt in Vt, admitting an
equivalent martingale measure. The aim of this note is to underline
the connection between this problem and the problems of asset
pricing in general discrete-time market models with portfolio
constraints and transaction costs. For the case of relatively open
convex sets Vt(ω) we present effective necessary and
sufficient conditions for the solvability of a suitably generalized
martingale selection problem. We show that this result allows to
obtain computationally feasible formulas for the price bounds of
contingent claims. For the case of currency markets we also sketch a
new proof of the first fundamental theorem of asset pricing.
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