Matrix majorization via vector majorization

Matrix majorization Geir Dahl

We study the conceptmatrix majorization: for two real matrices A and B having m rows we say that A majorizes B if there is a row-stochastic matrix X with AX = B. A special case is classical notion of vector majorization. Several properties and characterizations of matrix majorization are given. Moreover, interpretations of the concept in mathematical statistics are discussed and some combinator...

Weak matrix majorization

Given X, Y ∈ Rn×m we introduce the following notion of matrix majorization, called weak matrix majorization, X w Y if there exists a row-stochastic matrix A ∈ Rn×n such that AX = Y, and consider the relations between this concept, strong majorization ( s ) and directional majorization ( ). It is verified that s⇒ ⇒ w , but none of the reciprocal implications is true. Nevertheless, we study the i...

Linear preservers of two-sided matrix majorization

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Vector majorization and a robust option

We show that vector majorization and its related preference sets can be used to establish useful option pricing bounds for a robust option replacement investment strategy. This robust trading strategy can help to overcome some of the difficulties in implementing arbitrage option trading strategies when there exists model inaccuracy.

On Nonlinear Preservers of Weak Matrix Majorization