We present an approach and a system that explores the application of interactive machine learning to a branching program-based boosting algorithm—Martingale Boosting. Typically, its performance is based on the ability of a learner to meet a fixed objective and does not account for preferences (e.g., low FPs) arising from an underlying classification problem. We use user preferences gathered on ...

In a discrete-time financial market setting, the paper relates various concepts introduced for dynamic portfolios (both in discrete and in continuous time). These concepts are: value preserving portfolios, numeraire portfolios, interest oriented portfolios, and growth optimal portfolios. It will turn out that these concepts are all associated with a unique martingale measure which agrees with t...

Non-linear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the non-linear martingale problems under Lipschitz conditions on the coe cients. Mathematics Subject Classi cation (1991): 60G57, 60K35, 60J80.

We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. One also characterizes the optimal martingale measures and compute it explicitely in several examples.

We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of Lp-norm of a subordinated one via the same norm of a dominating one. In this setting this was done by Burkholder in [Bu1]–[Bu8]. If one of the martingales is orthogonal, the constant should drop. This was demonstrated in [BaJ1], when the orthogona...