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The Inverse Problem to the Question of the Existence of Interpolating Martingale Measuresстатья Исследовательская статья
- Авторы: Pavlov I.V., Danekyants A.G., Neumerzhitskaya N.V.
- Журнал: Communications on Stochastic Analysis
- Том: 14
- Номер: 3
- Год издания: 2020
- Издательство: LSU Digital Commons
- Местоположение издательства: Baton Rouge, LA, USA
- Первая страница: 89
- Последняя страница: 95
- Аннотация: In this paper, we formulate inverse problems that naturally arisewhen interpolating financial markets. Within the framework of this topic,one of the most important is the question of the existence of interpolationmartingale measures, introduced into consideration by the first co-author inthe 2000s. For static financial markets defined on finite or countable probabil-ity spaces, the inverse problem is formulated as follows: for a predeterminedprobability measure P and an initial condition a > 0, prove the existence of astock whose price at the initial moment coincides with a, and the measure Pfor the price process is an interpolation martingale measure. It is shown thatthis is true for finite probability spaces. For countable probability spaces,sufficient conditions are found for this statement to hold.
- Добавил в систему: Павлов Игорь Викторович