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作者：Broeker, Yannic; Mukherjee, Chiranjib
作者单位：University of Munster
摘要：We consider a Gaussian multiplicative chaos (GMC) measure on the classical Wiener space driven by a smoothened (Gaussian) space-time white noise. For d >= 3, it was shown in (Electron. Commun. Probab. 21 (2016) 61) that for small noise intensity, the total mass of the GMC converges to a strictly positive random variable, while larger disorder strength (i.e., low temperature) forces the total mass to lose uniform integrability, eventually producing a vanishing limit. Inspired by strong localiza...
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作者：Todorov, Viktor
作者单位：Northwestern University
摘要：We propose a nonparametric estimator of spot volatility from noisy short-dated option data. The estimator is based on forming portfolios of options with different strikes that replicate the (risk-neutral) conditional characteristic function of the underlying price in a model-free way. The separation of volatility from jumps is done by making use of the dominant role of the volatility in the conditional characteristic function over short time intervals and for large values of the characteristic...
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作者：Biagini, Francesca; Zhang, Yinglin
作者单位：University of Munich
摘要：In this paper, we introduce a sublinear conditional expectation with respect to a family of possibly nondominated probability measures on a progressively enlarged filtration. In this way, we extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other. Furthermore, we study the superhedging approach in continuous time for payment streams under model uncertainty, and est...
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作者：Hambly, Ben; Ledger, Sean; Sojmark, Andreas
作者单位：University of Oxford; University of Bristol
摘要：We study a McKean-Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier, they cause the other particles to jump in the direction of the barrier and this feedback mechanism leads to the possibility that the system can exhibit contagious blow-ups. Using a fixed-point argument, we construct a differentiable solution up to a first explosion time. Our main contribution is a proof of uniqueness in the class of cadlag functions, which ...
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作者：Carmona, Philippe; Petrelis, Nicolas
作者单位：Nantes Universite
摘要：In this paper we give a complete characterization of the scaling limit of the critical Interacting Partially Directed Self-Avoiding Walk (IPDSAW) introduced in Zwanzig and Lauritzen [J. Chem. Phys. 48 (1968) 3351]. As the system size L is an element of N diverges, we prove that the set of occupied sites, rescaled horizontally by L-2/3 and vertically by L-1/3 converges in law for the Hausdorff distance toward a nontrivial random set. This limiting set is built with a Brownian motion B condition...
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作者：Ding, Jian; Peres, Yuval; Ranade, Gireeja; Zhai, Alex
作者单位：University of Pennsylvania; Microsoft; Stanford University
摘要：We consider the stabilization of an unstable discrete-time linear system that is observed over a channel corrupted by continuous multiplicative noise. Our main result shows that if the system growth is large enough, then the system cannot be stabilized. This is done by showing that the probability that the state magnitude remains bounded must go to zero with time. Our proof technique recursively bounds the conditional density of the system state to bound the progress the controller can make. T...
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作者：Bion-Nadal, Jocelyne; Talay, Denis
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Inria; Universite Cote d'Azur
摘要：In this paper, we introduce a Wasserstein-type distance on the set of the probability distributions of strong solutions to stochastic differential equations. This new distance is defined by restricting the set of possible coupling measures. We prove that it may also be defined by means of the value function of a stochastic control problem whose Hamilton-Jacobi-Bellman equation has a smooth solution, which allows one to deduce a priori estimates or to obtain numerical evaluations. We exhibit an...
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作者：Conus, Daniel; Jentzen, Arnulf; Kurniawan, Ryan
作者单位：Lehigh University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates for numerical approximations of such SEEs have been investigated for about two decades and are far away from being well understood: roughly speaking, no essentially sharp weak convergence rates are known for parabolic SEEs with nonlinear diffusion c...
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作者：Bayraktar, Erhan; Budhiraja, Amarjit; Cohen, Asaf
作者单位：University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of Haifa
摘要：We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with its queue to minimize its expected cost. The rates and the cost functions in addition to depending on the control action, can depend, in a symmetric fashion, on the size of the individual queue and the empirical measure of the states of all queues in the syste...
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作者：Herrmann, Sebastian; Stebegg, Florian
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We consider the martingale optimal transport duality for cadlag processes with given initial and terminal laws. Strong duality and existence of dual optimizers (robust semistatic superhedging strategies) are proved for a class of payoffs that includes American, Asian, Bermudan and European options with intermediate maturity. We exhibit an optimal superhedging strategy for which the static part solves an auxiliary problem and the dynamic part is given explicitly in terms of the static part.
