Displaying similar documents to “Arbitrage in a simple model with general 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.

Incompleteness of the bond market with Lévy noise under the physical measure

Michał Barski (2015)

Banach Center Publications

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The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.

Discrete-time market models from the small investor point of view and the first fundamental-type theorem

Marek Karaś, Anna Serwatka (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we...