Matrix Representation of Martingale Measures with Quantized Marginals.

A stochastic process {St}t∈[0,T] is called a martingale process if E[SnΙSm] = Sm almost surely for all m ≤ n. Martingale processes are often used in arbitrage-free pricing of financial assets due to its "fair game" property, that is, when an asset is modeled using martingales then no one can consistently make or lose money through trades in that asset. In this paper, we focus our attention on random variables that follow a Pareto distribution. We then look at the set of martingale measures on Rℝ² having marginal measures which are quantized using the so-called Un-quantization. We shall then represent the transition kernel of such martingale measures as bistochastic matrices. Finally, we shall give some characterization of the set of such matrices. [ABSTRACT FROM AUTHOR]