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作者：Giles, Michael b.; Aji-ali, Abdul-lateef
作者单位：University of Oxford; Heriot Watt University; University of Edinburgh
摘要：We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of the underlying SDE that share parts of a Brownian path. Combining this new estimator with multilevel Monte Carlo (MLMC) leads to an estimator with a computational complexity that is similar to the complexity of a MLMC estimator when applied to options with Li...
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作者：Alon, Noga; Gunby, Benjamin; He, Xiaoyu; Shmaya, Eran; Solan, Eilon
作者单位：Princeton University; Rutgers University System; Rutgers University New Brunswick; State University of New York (SUNY) System; Stony Brook University; Tel Aviv University
摘要：A group of players are supposed to follow a prescribed profile of strategies. If they follow this profile, they will reach a given target. We show that if the target is not reached because some player deviates, then an outside observer can identify the deviator. We also construct identification methods in two nontrivial cases.
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作者：Avena, Luca; Capannol, Federico; Hazra, Rajat subhra; Quattropani, Matteo
作者单位：University of Florence; Leiden University - Excl LUMC; Leiden University; Sapienza University Rome
摘要：We consider the so-called directed configuration model (DCM), that is, a random directed graph with prescribed in- and out-degrees. In this random geometry, we study the meeting time of two random walks starting at stationarity, the coalescence time for a system of coalescent random walks, and the consensus time of the classical voter model. Indeed, it is known that the latter three quantities are related to each other under certain mean field conditions requiring fast enough mixing time and n...
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作者：Jacod, Jean; Lin, Huidi; Todorov, Viktor
作者单位：Sorbonne Universite; Universite Paris Cite; Northwestern University
摘要：In this paper we develop tests for detecting systematic jumps in asset prices of general form, including ones not explained by observable factors, and we further propose nonparametric estimates for them. The inference is based on a panel of high-frequency asset returns, with both the sampling frequency and the size of the cross-section increasing asymptotically. The feasible limit theory developed in the paper utilizes the different asymptotic roles played by diffusive versus jump risks and sy...
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作者：Bianchi, Alessandra; Collet, Francesca; Magnanini, Elena
作者单位：University of Padua; University of Verona; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together with a complete characterization of the phase diagram of the model. We borrow tools from statistical mechanics to obtain limit theorems for the edge density. First, we investigate the asymptotic distribution of this quantity, as the graph size tends to infin...
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作者：Ball, Frank; Sirl, David; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：We investigate final outcome properties of an SIR (susceptible -k infective -k recovered) epidemic model defined on a population of large subcommunities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of com...
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作者：Donoho, David l.; Kipnis, A. lon
作者单位：Stanford University; Reichman University
摘要：Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a p-value, we construct a global test against the joint null using the higher criticism (HC) statistics of these p-values. We calibrate the rare/weak model using parameters controlling the asymptotic distribution of nonnull p-values near zero. We derive a region in the parameter space wh...
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作者：Kim, Seonwoo; Sau, Federico
作者单位：Korea Institute for Advanced Study (KIAS); University of Trieste
摘要：We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulate...
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作者：Denisov, Denis; Wachtel, Vitali
作者单位：University of Manchester; University of Bielefeld
摘要：We consider a random walk in a truncated cone KN, which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study the behaviour of the Green function in this truncated cone as N increases. Using these results we also obtain the asymptotic behaviour of the harmonic The obtained results are applied to a multidimensional gambler's problem studied by Diaconis and Ethier (Staist. Sci. 37 (2022) 289-305). In particular we confirm their conjecture that the probability of e...
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作者：Sethi, Deven; Siska, David
作者单位：University of Edinburgh
摘要：The modified method of successive approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin optimality principle which, starting with an initial open loop control, solves the forward equation, the backward adjoint equation and then performs a static minimization step. We observe that this is an implicit Euler scheme for a gradient flow system. We prove that appropriate interpolations of the iterates of the modi...
