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作者：Liu, Yuping; Ma, Jin
作者单位：University of Southern California
摘要：In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is non-Markovian in general. The insurance company c...
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作者：du Toit, Jacques; Peskir, Goran
作者单位：University of Manchester
摘要：Assuming that the stock price Z = (Z(t))(0 <= t <= T) follows a geometric Brownian motion with drift mu is an element of R and volatility sigma > 0, and letting M-t = max(0 <= s <= t) Z(s) for t is an element of [0, T], we consider the optimal prediction problems V-1 = inf(0 <=tau <= T) E(M-T/Z(tau)) and V-2 = sup(0 <=tau <= T) E(Z(tau)/M-T), where the infimum and supremum are taken over all stopping times tau of Z. We show that the following strategy is optimal in the first problem: if mu <= ...
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作者：Greven, Andreas; Popovic, Lea; Winter, Anita
作者单位：University of Erlangen Nuremberg; Concordia University - Canada
摘要：We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate proportional to the number of catalyst individuals alive. The reactant forms a process in random medium. We describe asymptotically the genealogy of catalytic branching populations coded as the induced forest of R-trees using the many individuals-rapid branch...
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作者：Holden, Lars; Hauge, Ragnar; Holden, Marit
摘要：We propose an adaptive independent Metropolis-Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis-Hastings algorithm. Convergence is proved provided a strong Doeblin condition is satisfied, which essentially requires that all the proposal functions have uniformly heavier tails than the stationary distribution. The proof also holds if proposals depending on the current state are used ...
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作者：Teixeira, Augusto
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the model of random interlacements on Z(d) introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in a of the probability that the origin belongs to the infinite component of the vacant set at level a in the supercritical phase u < u*.
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作者：Yatracos, Yannis G.
作者单位：National University of Singapore
摘要：In a sample variance decomposition, with components functions of the sample's spacings, the largest component (I) over tilde (n) is used in cluster detection. It is shown for normal samples that the asymptotic distribution of (I) over tilde (n) is the Gumbel distribution.
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作者：Rataj, Jan; Spodarev, Evgeny; Meschenmoser, Daniel
作者单位：Charles University Prague; Ulm University
摘要：A parallel neighborhood of a path of a Brownian motion is sometimes called the Wiener sausage. We consider almost sure approximations of this random set by a sequence of random polyconvex sets and show that the convergence of the corresponding mean curvature measures holds under certain conditions in two and three dimensions. Based on these convergence results, the mean curvature measures of the Wiener sausage are calculated numerically by Monte Carlo simulations in two dimensions. The corresp...
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作者：Pemantle, Robin
作者单位：University of Pennsylvania
摘要：Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean p <= 1/2. How many of these Bernoullis one must look at in order to find a path of length n from the root which maximizes, up to a factor of 1 - epsilon, the sum of the Bernoullis along the path? In the case p = 1/2 (the critical value for nontriviality), it is shown to take Theta(epsilon(-1)n) steps. In the case p < 1/2, the number of steps is shown to be at least n exp(const epsilon...
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作者：Durrett, Rick; Popovic, Lea
作者单位：Cornell University; Concordia University - Canada
摘要：We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745-766] double recessive null model and lynch and Force's [Genetics 154 (2000) 459-473] subfunctionalization model. Though the state spaces of these diffusions are two and six-dimensional, respectively, we show in each case that the diffusion stays close to a curve. Using ideas of Katzenberger [Ann. Probab. 19 (1991) 1587-1628] we show that one-dimensional projections converge to diffusio...
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作者：Gromoll, H. Christian; Williams, Ruth J.
作者单位：University of Virginia; University of California System; University of California San Diego
摘要：We consider a stochastic model of Internet congestion control, introduced by Massoulie and Roberts [telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows in a network where bandwidth is shared among document transfers. In contrast to an ear lier work by Kelly and Williams [Ann. Appl. Probab. 14 (2004) 1055-1083], the present paper allows interarrival times and document sires to be generally distributed, rather than exponentially distributed. Further...
