Displaying similar documents to “The martingale method of shortfall risk minimization in a discrete time market”

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.

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...

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....

Optimal investment under behavioural criteria - a dual approach

Miklós Rásonyi, José G. Rodríguez-Villarreal (2015)

Banach Center Publications

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We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in Carassus-Rásonyi (2015) under certain conditions on the parameters of these power functions. In the present paper we prove the existence of optimal strategies under a different set of conditions on the parameters, identical to the ones in Rásonyi-Rodrigues...

A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque, Chuan-Hsiang Han (2007)

ESAIM: Probability and Statistics

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A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving...