A note on convex ordering for stable stochastic integrals

Abstract

We establish a convex ordering between stochastic integrals driven by strictly α-stable processes with index α ∈ (1,2). Our approach is based on the forward–backward stochastic calculus for martingales together with a suitable decomposition of stable stochastic integrals.

Keywords::

• stable process
• stable stochastic integral
• convex ordering
• forward–backward stochastic calculus

MSC (2010) Classification::

• 60G52
• 60H05
• 60E15
• 60G44

Acknowledgements

The authors thank Yutao Ma for useful discussions. They are also grateful to the French Agency Campus France for financial support.