Assume that X, Y are martingales such that Y is differentially subordinate to X and X [member of] [L.
t]] [greater than or equal to] 1} and the stopped martingales [X.
valid for all real martingales f and their transforms g by predictable sequences bounded in absolute value by 1.
DELTA],C](t) be the wealth process of a portfolio [DELTA] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is a locally integrable Martingale.
15) is locally integrable Martingale under a real world probability measure P, then
0] [LAMBDA](s)C(s)ds is also locally integrable Martingale under a real world probability measure P.
Based on this polynomial we will find a family of martingales and obtain convergence results for these by well-known properties in the branching random walk.
Obviously there is an easy connection between the two martingales.
Continuous Exponential Martingales and BMO, Springer-Verlag, Lecture Notes in Mathematics No.
A Criterion for Uniform Integrability of Exponential Martingales, Tohoku Mathematical Journal, 34:495-498, 1982.
Muller, 1989, "On Complete Securities Markets and the Martingale Property of Securities Prices", Economics Letters, 31:37-41
Ross, 1989, "Information and Volatility--The No-Arbitrage Martingale Approach to Timing and Resolution Irrelevancy", Journal of Finance, 44:1-17