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Adapted Wasserstein distances and stability in mathematical finance
Assume that an agent models a financial asset through a measure ℚ with the goal to
price/hedge some derivative or optimise some expected utility. Even if the model ℚ is …
price/hedge some derivative or optimise some expected utility. Even if the model ℚ is …
Existence, duality, and cyclical monotonicity for weak transport costs
The optimal weak transport problem has recently been introduced by Gozlan et al.(J Funct
Anal 273 (11): 3327–3405, 2017). We provide general existence and duality results for …
Anal 273 (11): 3327–3405, 2017). We provide general existence and duality results for …
All adapted topologies are equal
A number of researchers have introduced topological structures on the set of laws of
stochastic processes. A unifying goal of these authors is to strengthen the usual weak …
stochastic processes. A unifying goal of these authors is to strengthen the usual weak …
The Wasserstein space of stochastic processes
Wasserstein distance induces a natural Riemannian structure for the probabilities on the
Euclidean space. This insight of classical transport theory is fundamental for tremendous …
Euclidean space. This insight of classical transport theory is fundamental for tremendous …
Martingale Benamou–Brenier
In classical optimal transport, the contributions of Benamou–Brenier and McCann regarding
the time-dependent version of the problem are cornerstones of the field and form the basis …
the time-dependent version of the problem are cornerstones of the field and form the basis …
Stability of martingale optimal transport and weak optimal transport
Under mild regularity assumptions, the transport problem is stable in the following sense: if a
sequence of optimal transport plans π 1, π 2,… converges weakly to a transport plan π, then …
sequence of optimal transport plans π 1, π 2,… converges weakly to a transport plan π, then …
Denseness of adapted processes among causal couplings
M Beiglböck, D Lacker - ar** via distribution regression: a higher rank signature approach
B Horvath, M Lemercier, C Liu, T Lyons… - ar** the
law of a stochastic process to a scalar target. The learning procedure based on the notion of …
law of a stochastic process to a scalar target. The learning procedure based on the notion of …
Continuity of the martingale optimal transport problem on the real line
J Wiesel - The Annals of Applied Probability, 2023 - projecteuclid.org
We show continuity of the martingale optimal transport optimisation problem as a functional
of its marginals. This is achieved via an estimate on the projection in the nested/causal …
of its marginals. This is achieved via an estimate on the projection in the nested/causal …