Some norm estimates for semimartingales

Abstract

In this paper we introduce a new type of norms for semimartingales, under both linear and nonlinear expectations. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games [21], whose value process is conjectured to be a semimartingale under a class of probability measures. As a by product, we establish some a priori estimates for doubly reflected BSDEs without imposing the Mokobodski's condition directly.

Solving finite time horizon Dynkin games by optimal switching

“…Moreover, using Lemma 1 (Mokobodski's hypothesis) and [22,Theorem 3.4], for instance, we also know that (V T , ζ T , K T ) is, modulo indistinguishability, the unique solution to (24) in this instance.…”

“…Pham and Zhang [22,Theorem 3.4] verified that the norm (L, U ) T 0 is finite, and it is not difficult to…”

Nash Equilibrium Payoffs for Stochastic Differential Games with two Reflecting Barriers

“…We now provide the following estimate of the solutions of BSDEs with two reflecting barriers, which plays an important role in this paper. Since some of the proof technique is derived from Pham and Zhang [15], we omit the proof here.…”

Radner Equilibria Under Ambiguous Volatility

“…44 As defined in Pham and Zhang (2012), the uncertain process S is a P-semimartingale if it is a P -semimartingale for every P ∈ P. Note that their Assumption 4.1 is in the present setting fulfilled, since we augment the filtration with the P-polar sets.…”