Abstract
In the first part of the paper, we construct the models of the complete non-arbitrage financial markets for a wide class of evolutions of risky assets.This construction is based on the observation that for a certain class of risky as set evolutions the martingale measure is invariant with respect to these evolutions. For such a financial market model the only martingale measure being equivalent to an initial measure is built. On such a financial market,formulas for the fair price of contingent liabilities are presented. A multi-parameter model of the financial market is proposed, the martingale measure of which does not depend on the parameters of the model of the evolution of risky assets and is the only one.
Highlights
In this paper, models of non-arbitrage markets are constructed on the basis of the invariance of a set of spot measures with respect to a certain class of evolution of risky assets
This construction is based on the observation that for a certain class of risky asset evolutions the martingale measure is invariant with respect to these evolutions
For such a financial market model the only martingale measure being equivalent to an initial measure is built
Summary
Models of non-arbitrage markets are constructed on the basis of the invariance of a set of spot measures with respect to a certain class of evolution of risky assets. With the appearance of the work [1], which proposes a regular method for describing all martingale measures for a wide class of evolutions of risky assets [22], [23], [24] that capture the phenomenon of price memory and clustering, it became possible to construct realistic models of non-arbitrage markets. Note that such efforts have been made in this direction, and more about this can be found in the monograph [13], [14]. This will allow the computer to be used to model the financial market
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