Модель опционов в терминах процессов леви

Модель опционов в терминах процессов леви

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Содержание:

Christophe Stricker This paper defines an optimization criterion for the set of all martingale measures for an incomplete модель опционов в терминах процессов леви model when the discounted price process is bounded and quasi-left continuous.

модель опционов в терминах процессов леви владимир соловьев биткоин

This criterion is based on the entropy-Hellinger process for a nonnegative Doleans-Dade exponential local martingale. We develop properties of this process and establish its relationship to the relative entropy distance.

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We prove that the martingale measure, minimizing this entropy-Hellinger process, is unique. Furthermore, it exists and is explicitly determined under some mild conditions of integrability and no arbitrage.

модель опционов в терминах процессов леви примеры задач опционы

Different characterizations for this extremal risk-neutral measure as well as immediate application to the exponential hedging are given. If the discounted price process is continuous, the minimal entropy-Hellinger martingale measure simply is the minimal martingale measure of Follmer and Schweizer.

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Finally, the relationship between the minimal entropy-Hellinger martingale measure MHM and the minimal entropy martingale measure MEM is provided. We also give an example showing that in contrast to the MHM measure, the MEM measure is not robust with respect to stopping.

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