APPLYING ITO'S MOTTO: "LOOK AT THE INFINITE DIMENSIONAL PICTURE" BY CONSTRUCTING SHEETS TO OBTAIN PROCESSES INCREASING IN THE CONVEX ORDER

作者：Hirsch Francis^*; Roynette Bernard; Yor Marc

来源：Periodica Mathematica Hungarica, 2010, 61(1-2): 195-211.

DOI：10.1007/s10998-010-3195-8

• convex order
• 1-martingale
• PCOC
• Levy sheet
• Sato sheet
• Gaussian sheet

Strongly inspired by the result due to Carr-Ewald-Xiao that the arithmetic average of geometric Brownian motion is an increasing process in the convex order, we extend this result to integrals of L,vy processes and Gaussian processes. Our method consists in finding an appropriate sheet associated to the original L,vy or Gaussian process, from which the one-dimensional marginals of the integrals will appear to be those of a martingale, thus proving the increase in the convex order property.

• 出版日期2010-9