A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion.
A comparison theorem for semimartingales and its applications
A continuous martingale in the plane that may spiral away to infinity
A counterexample related to -weights in martingale theory
A family of integral representations for the brownian variables
A family of non-Gaussian martingales with Gaussian marginals.
A general version of the fundamental theorem of asset pricing.
A Hilbert transform for non-homogeneous martingales
A local time inequality for martingales
A martingale approach to some Wiener-Hopf problems, I
A martingale approach to some Wiener-Hopf problems, II
A martingale control variate method for option pricing with stochastic volatility
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...
A martingale proof of the Khinchin iterated logarithm law for Wiener processes
A maximal inequality for martingale local times
A new kind of augmentation of filtrations
Let (Ω, , ()t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (theσ-algebra generated by ()t≥0) a coherent family of probability measures () indexed byt≥0, each of them being defined on . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....
A new kind of augmentation of filtrations
Let (Ω, , ()t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (the σ-algebra generated by ()t≥0) a coherent family of probability measures () indexed by t≥0, each of them being defined on . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A note on dilations and martingales.
A note on inhomogeneous continuous-state branching processes