On Krylov’s estimates for optional semimartingales

Some norm estimates for semimartingales

In this paper we introduce a new type of norm for semimartingales. 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, whose value process we conjecture to be a semimartingale under a class of probability measures under some conditions. The norm introduced he...

Optional decomposition for continuous semimartingales under arbitrary filtrations

We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).

On the jump activity index for semimartingales

Empirical evidence of asset price discontinuities or ‘‘jumps’’ in financial markets has been well documented in the literature. Recently, Aït-Sahalia and Jacod (2009b) defined a general ‘‘jump activity index’’ to describe the degree of jump activities for asset price semimartingales, and provided a consistent estimatorwhen the underlying process contains both a continuous and a jump component. ...

Smoothing Signals for Semimartingales

Hedging contingent claims on semimartingales

This paper extends the known results on the equivalence between market completeness and the uniqueness of martingale measures for finite asset economies, to the infinite asset case. Our arguments employ results from the theory of linear operators between locally convex topological vector spaces. This theory of linear operators provides an operational approach to the issue of completeness and un...