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Martingale selection problem and asset pricing in finite discrete time


 
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1. Title Title of document Martingale selection problem and asset pricing in finite discrete time
 
2. Creator Author's name, affiliation, country Dmitry B. Rokhlin; Rostov State University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) martingale selection, arbitrage, price bounds, constraints, transaction costs
 
3. Subject Subject classification 60G42; 91B24
 
4. Description Abstract Given a set-valued stochastic process $(V_t)_{t=0}^T$, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $\xi_t\in V_t$, 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 $V_t(\omega)$ 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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7. Date (YYYY-MM-DD) 2007-01-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1240
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1240
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
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