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作者：Xu, Lihu
作者单位：University of Macau
摘要：Let n is an element of N, let zeta(n,1), . . . , zeta(n,n) be a sequence of independent random variables with E zeta(n,i) = 0 and E vertical bar zeta(n,i)vertical bar < infinity for each i, and let mu be an alpha-stable distribution having characteristic function e(-vertical bar lambda vertical bar alpha) with alpha is an element of (1, 2). Denote S-n = zeta(n,1) + . . . + zeta(n,n) and its distribution by L (S-n), we bound the Wasserstein-1 distance of L(S-n) and mu essentially by an L-1 disc...
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作者：Bank, Peter; Dolinsky, Yan
作者单位：Technical University of Berlin; Hebrew University of Jerusalem; Monash University
摘要：We establish a superreplication duality in a continuous-time financial model as in (Bank and Vo beta (2018)) where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an exponential rate Similar to the literature on models with a constant spread (cf., e.g., Math. Finance 6 (1996) 133-165; Ann. Appl. Probab. 20 (2010) 1341-1358; Ann. Appl. Probab. 27 (2017) 1414-1451), our dual description of su...
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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...
