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作者：Fuhrman, Marco; Huyen Pham
作者单位：Polytechnic University of Milan; Universite Paris Cite
摘要：We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with...
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作者：Bertacchi, Daniela; Zucca, Fabio
作者单位：University of Milano-Bicocca; Polytechnic University of Milan
摘要：In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on Z(d) survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process when restricted to the infinite percolation cluster Coo of a supercritical Bernoulli percolation. When no more than k individuals per site are allowed, we obtain the k-type contact process, which can be derived from the branching random walk by killing all particles that...
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作者：Gassiat, Paul; Mijatovic, Aleksandar; Oberhauser, Harald
作者单位：Technical University of Berlin; Imperial College London; University of Oxford
摘要：We derive a nonlinear integral equation to calculate Root's solution of the Skorokhod embedding problem for atom-free target measures. We then use this to efficiently generate bounded time space increments of Brownian motion and give a parabolic version of Muller's classic Random walk over spheres algorithm.
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作者：Delarue, Francois; Inglis, James; Rubenthaler, Sylvain; Tanre, Etienne
作者单位：Universite Cote d'Azur; Universite Cote d'Azur
摘要：We here investigate the well-posedness of a networked integrate-and-fire model describing an infinite population of neurons which interact with one another through their common statistical distribution. The interaction is of the self-excitatory type as, at any time, the potential of a neuron increases when some of the others fire: precisely, the kick it receives is proportional to the instantaneous proportion of firing neurons at the same time. From a mathematical point of view, the coefficien...
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作者：Kardaras, Constantinos; Kreher, Doerte; Nikeghbali, Ashkan
作者单位：University of London; London School Economics & Political Science; Humboldt University of Berlin; University of Zurich; University of Zurich
摘要：This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine the default term apparent in risk-neutral option prices if the underlying stock exhibits a bubble modeled by a strict local martingale. Results for certain path dependent options and last passage time formulas are given.
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作者：Avram, F.; Palmowski, Z.; Pistorius, M. R.
作者单位：Universite de Pau et des Pays de l'Adour; University of Wroclaw; Imperial College London
摘要：This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative Levy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin, which is an increasing function of the size of...
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作者：Bhamidi, Shankar; Goodman, Jesse; van der Hofstad, Remco; Komjathy, Julia
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Technion Israel Institute of Technology; Eindhoven University of Technology
摘要：In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large degrees of this tree and compare it to the degree distribution of the original graph. We perform this analysis for the complete graph with edge weights that are powers of exponential random variables (weak disorder in the stochastic mean-field model of distance)...
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作者：Ma, Jin; Wu, Zhen; Zhang, Detao; Zhang, Jianfeng
作者单位：University of Southern California; Shandong University
摘要：In this paper, we study the well-posedness of the Forward Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental long-standing problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is...
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作者：Cerf, Raphael
作者单位：Universite Paris Saclay
摘要：We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size m of chromosomes of length l over an alphabet of cardinality kappa. The mutation probability per locus is q. The replication rate is sigma > 1 for the master sequence and 1 for the other sequences. We study the equilibrium distribution of the process in the regime where l -> +infinity, m -> +infinity, q -> 0, l(q) -> a...
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作者：Guasoni, Paolo; Rasonyi, Miklos
作者单位：Boston University; Dublin City University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Edinburgh
摘要：In a continuous-time model with multiple assets described by cadlag processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalab...
