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作者：Bion-Nadal, Jocelyne; Kervarec, Magali
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Saclay
摘要：The framework of this paper is that of risk measuring under uncertainty which is when no reference probability measure is given. To every regular convex risk measure on C-b(Omega), we associate a unique equivalence class of probability measures on Borel sets, characterizing the riskless nonpositive elements of C-b(Omega). We prove that the convex risk measure has a dual representation with a countable set of probability measures absolutely continuous with respect to a certain probability measu...
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作者：Burnashev, Marat V.; Tchamkerten, Aslan
作者单位：Russian Academy of Sciences; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
摘要：Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time tau(l) of a given level l with a stopping time eta defined over the noisy observation process. Main results are upper and lower bounds on the minimum mean absolute deviation in f(eta) E vertical bar eta - tau(l)vertical bar which become tight as l -> infinity. Interestingly, in this regime the estimation error does not get smaller if we a...
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作者：Neal, Peter; Roberts, Gareth; Yuen, Wai Kong
作者单位：University of Manchester; University of Warwick; Brock University
摘要：We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous target densities. The main result is a weak convergence result as the dimensionality d of the target densities converges to infinity. In particular, when the proposal variance is scaled by d(-2), the sequence of stochastic processes formed by the first compone...
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作者：Bayraktar, Erhan; Huang, Yu-Jui; Song, Qingshuo
作者单位：University of Michigan System; University of Michigan; City University of Hong Kong
摘要：Our goal is to resolve a problem proposed by Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of initial capital with which an investor can beat the market portfolio with a certain probability, as a function of the market configuration and time to maturity. We show that this value function is the smallest nonnegative viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On optimal arbitrage (2008) Columbia Univ.], we do n...
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作者：Cisse, Mamadou; Patie, Pierre; Tanre, Etienne
作者单位：Universite Libre de Bruxelles; Universite Cote d'Azur
摘要：In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93-108] and [Tear. Veroyatn. Primen. 45 (2000) 657-669] and Irles and Paulsen [Sequential Anal. 23 (2004) 297-316]. Our approach relies on a combination of techniques borrow...
