Displaying similar documents to “Discrete time arbitrage under transaction costs”

On Existence of Local Martingale Measures for Insiders who Can Stop at Honest Times

Jakub Zwierz (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time Λ. We show, using the multiplicative decomposition of the Azéma supermartingale, that if the martingale part of the price process has the predictable representation property and Λ satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider....

The martingale method of shortfall risk minimization in a discrete time market

Marek Andrzej Kociński (2012)

Applicationes Mathematicae

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The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.

Arbitrage in a simple model with general transaction costs

Jakub Olejnik (2005)

Applicationes Mathematicae

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We study a version of no arbitrage condition in a simple model with general transaction costs. Our condition is equivalent to the existence of an equivalent martingale measure.

Elementary stochastic calculus for finance with infinitesimals

Jiří Witzany (2017)

Commentationes Mathematicae Universitatis Carolinae

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The concept of an equivalent martingale measure is of key importance for pricing of financial derivative contracts. The goal of the paper is to apply infinitesimals in the non-standard analysis set-up to provide an elementary construction of the equivalent martingale measure built on hyperfinite binomial trees with infinitesimal time steps.