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作者：Ball, Frank G.; Sirl, David J.; Trapman, Pieter
作者单位：University of Nottingham; Loughborough University; Stockholm University
摘要：In this paper we consider a model for the spread of a stochastic SIR (Susceptible -> Infectious -> Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of cliques, each of random size, and infection can be transmitted between two individuals if and only if there is a clique they both belong to. Both the clique sizes and the number of cliques an individual belongs to follow mixed Poisson distributions. An infinite-type b...
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作者：Rosenbaum, Mathieu; Tankov, Peter
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Cite
摘要：In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkhauser/Springer Basel AG] for continuous processes, we propose a framework enabling us to (asymptotically) optimize the discretization times. More precisely, a discretization rule is said to be optimal if for a given cost function, no strategy has (asymptotically, for large cost) a lower mean...
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作者：Fontes, L. R. G.; Gava, R. J.; Gayrard, V.
作者单位：Universidade de Sao Paulo; Universidade Federal de Sao Carlos; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We introduce trap models on a finite volume k-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters of the trap model, we establish its infinite volume limit, given by what we call a K-process in an infinite k-level tree. From this we deduce that the K-process also is the scaling limit of the GREM-like trap model on extreme time scales under a fin...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：Let Z = (Z(t))(t >= 0) be a regular diffusion process started at 0, an independent random variable with a strictly increasing and continue:.stribution function F, and let tau(l) = inf{t >= 0 vertical bar Z(t) = l} be the first entry, ... of Z at the level l. We show that the quickest detection problem tau sup E[R-tau - (0)integral(tau) c(R-t) dt], where R = S I is the range process of X = 2F(Z) 1 (i.e., the difference between the running maximum and the running minimum of X) and c(r) = cr with...
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作者：Jin, Baisuo; Wang, Chen; Bai, Z. D.; Nair, K. Krishnan; Harding, Matthew
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore; Northeast Normal University - China; Northeast Normal University - China; Stanford University; Stanford University
摘要：This paper studies the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix. The auto-cross covariance matrix is defined as M-tau = 1/2T Sigma(T)(j=1) (e(j) e(j+tau)*+ e(j+tau)e(j)*) where e(j) is an N dimensional vectors of independent standard complex components with properties stated in Theorem 1.1, and tau is the lag. M-0 is well studied in the literature whose LSD is the Mareenko-Pastur (MP) Law. The contribution of this paper is in determining the LSD of M-t...
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作者：Faggionato, A.; Roberto, C.; Toninelli, C.
作者单位：Sapienza University Rome; Universite Paris Nanterre; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We consider one-dimensional hierarchical coalescence processes (in short HCPs) where two or three neighboring domains can merge. An HCP consists of an infinite sequence of stochastic coalescence processes: each process occurs in a different epoch and evolves for an infinite time, while the evolutions in subsequent epochs are linked in such a way that the initial distribution of epoch n + 1 coincides with the final distribution of epoch n. Inside each epoch a domain can incorporate one of its n...
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作者：Pulido, Sergio
作者单位：Carnegie Mellon University
摘要：This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuoustime financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a wellknown result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of maximality of contingent claims.
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作者：Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F.
作者单位：Ruprecht Karls University Heidelberg; University of Bern
摘要：This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Ito semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.
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作者：Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or non-Markovian) case for a general stochastic control problem. A general convergence result is obtained by a weak convergence method in the spirit of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time (1992) Springer]. We also get a r...
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作者：Ouchard, Bruno B.; Moreau, Ludovic; Nutz, Marcel
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian unce...
