Strict Local Martingales With Jumps
نویسنده
چکیده
A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of “naturally occurring” strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a phenomenon we would contend is common in applications such as filtering, control, and especially in mathematical finance. We give a method for constructing such examples and analyze one particular method in detail.
منابع مشابه
Optimal Novikov-type criteria for local martingales with jumps
We consider càdlàg local martingales M with initial value zero and jumps larger than a for some a larger than or equal to −1, and prove Novikov-type criteria for the exponential local martingale to be a uniformly integrable martingale. We obtain criteria using both the quadratic variation and the predictable quadratic variation. We prove optimality of the coefficients in the criteria. As a coro...
متن کاملAnalysis of continuous strict local martingales via h-transforms
We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer [7]. Although nonnegative local martingales are supermartingales, we identify a class of convex functions which when applied to such local martingales produce submartingales. We extend part of this analysis to conformal local martingales in dimensions three and higher. An interesting conne...
متن کاملStrict Local Martingales, Bubbles, and No Early Exercise
We show pathological behavior of asset price processes modeled by continuous strict local martingales under a risk-neutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monot...
متن کاملA Visual Criterion for Identifying Itô Diffusions as Martingales or Strict Local Martingales
It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our main theorem demonstrates that the qu...
متن کاملA Central Limit Theorem for Local Martingales with Applications to the Analysis of Longitudinal Data
SUMMARY A functional central limit theorem for a local square integrable martingale with persistent disconti-nuities is given. By persistent discontinuities, it is meant that the martingale has jumps which do not vanish asymptotically. This central limit theorem is motivated by problems in the analysis of longitudinal and life history data.
متن کامل