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作者：Beskos, A; Roberts, GO
作者单位：Lancaster University
摘要：We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random collection of time instances. The path can then be completed without further reference to the dynamics of the target process.
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作者：Kouritzin, MA; Sun, W
作者单位：University of Alberta; Concordia University - Canada
摘要：Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t -> X-t is a Markov process and we wish to calculate the measure-valued process t -> mu(t) ((.)) = P{X-t is an element of (.)vertical bar sigma{Y-tk,Y- t(k) <= t}} where tk =k epsilon and Y-tk is a distorted, corrupted, partial observation of Xt(k). Then, one constructs a particle system with observation-dependent branching and n initial particl...
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作者：Yan, LQ
作者单位：State University System of Florida; University of Florida
摘要：A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semi martingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SIDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumption on their finite variation part. The asymptotic behavior (weak convergence) of the normalized erro...
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作者：del Moral, P; Garnier, J
作者单位：Universite Cote d'Azur; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
摘要：In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman-Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algori...
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作者：Bouchard, B; Pham, H
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Institut Polytechnique de Paris; ENSAE Paris
摘要：We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and Rasonyi Finance and Stochastics 7 (2003) 403-411] and [Schachermayer Math. Finance 14 (2004) 19-48]. In addition to the usual investment in financial assets, we assume that the agents can invest part of their wealth in industrial projects that yield a nonlinear random return. We study the problem of maximizing the utility of consumption on a finite time period. The main difficu...
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作者：Harrison, JM; Williams, RJ
作者单位：Stanford University; University of California System; University of California San Diego
摘要：We consider a dynamic control problem associated with a generalized Brownian network, the objective being to minimize expected discounted cost over an infinite planning horizon. In this Brownian control problem (BCP), both the system manager's control and the associated cumulative cost process may be locally of unbounded variation. Due to this aspect of the cost process, both the precise statement of the problem and its analysis involve delicate technical issues. We show that the BCP is equiva...
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作者：De Donno, M; Pratelli, M
作者单位：University of Pisa
摘要：We introduce a theory of stochastic integration with respect to a family of sernimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.
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作者：Hult, H; Lindskog, F; Mikosch, T; Samorodnitsky, G
作者单位：Cornell University; Royal Institute of Technology; University of Copenhagen
摘要：We extend classical results by A. V. Nagaev [Izv Akad. Nauk UzSSR Ser Fiz.-Mat. Nauk 6 (1969) 17-22, Theory Probab. Appl. 14 (1969) 51-64, 193-208] on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of cAdlAg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin...
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作者：Bouchard, B; El Karoui, N; Touzi, N
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; ENSAE Paris; Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine
摘要：We study a maturity randomization technique for approximating optimal control problems. The algorithm is based on a sequence of control problems with random terminal horizon which converges to the original one. This is a generalization of the so-called Canadization procedure suggested by Carr [Review of Financial Studies II (1998) 597-626] for the fast computation of American put option prices. In addition to the original application of this technique to optimal stopping problems, we provide a...
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作者：Mohamed, H; Robert, P
作者单位：Inria
摘要：In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. This approach gives a unified probabilistic treatment of these questions. It simplifies and extends some of the results known in this domain.
