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作者：Davis, Erik; Sethuraman, Sunder
作者单位：University of Arizona
摘要：Given a cost functional F on paths gamma in a domain D subset of R-d, in the form 1 F(gamma) = integral(1)(0) f (gamma(t), gamma(t)) dt , it is of interest to approximate its minimum cost and geodesic paths. Let X-1,...X-n be points drawn independently from D according to a distribution with a density. Form a random geometric graph on the points where X-i and X-j are connected when 0 < vertical bar X-i - X-j vertical bar < epsilon, and the length scale epsilon = epsilon(n) vanishes at a suitab...
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作者：Leite, Saul C.; Williams, Ruth J.
作者单位：Universidade Federal do ABC (UFABC); University of California System; University of California San Diego
摘要：Continuous-time Markov chain models are often used to describe the stochastic dynamics of networks of reacting chemical species, especially in the growing field of systems biology. These Markov chain models are often studied by simulating sample paths in order to generate Monte-Carlo estimates. However, discrete-event stochastic simulation of these models rapidly becomes computationally intensive. Consequently, more tractable diffusion approximations are commonly used in numerical computation,...
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作者：Bartl, Daniel
作者单位：University of Konstanz
摘要：We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martinga...
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作者：Benaim, Michel; Strickler, Edouard
作者单位：University of Neuchatel
摘要：Let E be a finite set, {F-i}(i is an element of E) a family of vector fields on R-d leaving positively invariant a compact set M and having a common zero p is an element of M. We consider a piecewise deterministic Markov process (X, I) on M x E defined by (X)over dot(t)=F(I)t(X-t) where I is a jump process controlled by X: Pr(It+s = j vertical bar(X-u ,I-u)(u <= t)) = a(ij)(X-t)(s) + o(s) for i not equal j on {I-t=i}. We show that the behaviour of (X, I) is mainly determined by the behaviour o...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：We first show that a smooth fit between the value function and the gain function at the optimal stopping boundary for a two-dimensional diffusion process implies the absence of boundary's discontinuities of the first kind (the right-hand and left-hand limits exist but differ). We then show that the smooth fit itself is satisfied over the flat portion of the optimal stopping boundary arising from any of its hypothesised jumps. Combining the two facts we obtain that the optimal stopping boundary...
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作者：Blancas, Airam; Rogers, Tim; Schweinsberg, Jason; Siri-Jegousso, Arno
作者单位：Goethe University Frankfurt; University of Bath; University of California System; University of California San Diego; Universidad Nacional Autonoma de Mexico
摘要：The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time t decays as 2 gamma/ct(2), where c is the ratio of the coalescence rates at the individual and species levels, and t...
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作者：Bakhtin, Yuri; Pajor-Gyulai, Zsolt
作者单位：New York University
摘要：For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.
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作者：Tsukuda, Koji
作者单位：University of Tokyo
摘要：The Ewens sampling formula was first introduced in the context of population genetics by Warren John Ewens in 1972, and has appeared in a lot of other scientific fields. There are abundant approximation results associated with the Ewens sampling formula especially when one of the parameters, the sample size n or the mutation parameter theta which denotes the scaled mutation rate, tends to infinity while the other is fixed. By contrast, the case that theta grows with n has been considered in a ...
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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...
