Stochastics and Stochastic Reports最新文献

Importance Sampling, Large Deviations, and Differential Games 重要性抽样，大偏差和微分对策

Stochastics and Stochastic Reports Pub Date : 2004-12-01 DOI: 10.1080/10451120410001733845

P. Dupuis, Hui Wang

{"title":"Importance Sampling, Large Deviations, and Differential Games","authors":"P. Dupuis, Hui Wang","doi":"10.1080/10451120410001733845","DOIUrl":"https://doi.org/10.1080/10451120410001733845","url":null,"abstract":"A standard heuristic in the area of importance sampling is that the changes of measure used to prove large deviation lower bounds give good performance when used for importance sampling. Recent work, however, has shown that a naive implementation of the heuristic is incorrect in many situations. The present paper considers the simple setting of sums of independent and identically distributed (iid) random variables, and shows that under mild conditions asymptotically optimal changes of measure can be found if one considers dynamic importance sampling schemes. For such schemes, the change of measure applied to an individual summand can depend on the historical empirical mean of the simulation (i.e. the system state). In analyzing the asymptotic performance of importance sampling, we show that the value function of a differential game characterizes the optimal performance, with player A corresponding to the choice of change of measure and player B arising due to a large deviations analysis. From this perspective, the traditional implementation of the heuristic is shown to correspond to player A choosing a control that is fixed, regardless of the system state or player B's choice of control. This leads to an \"open loop\" control for player A, which is suboptimal except in special cases. Our final contribution is a method, based on the Isaacs equation associated with the differential game, for constructing dynamic schemes. Numerical examples are presented to illustrate the results.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"249 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114543765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 167

Hyperfinite Lévy Processes 超有限lsamvy过程

Stochastics and Stochastic Reports Pub Date : 2004-12-01 DOI: 10.1080/10451120412331315797

T. Lindstrøm

引用次数: 22

Spread of branching diffusion: Sharp asymptotics 分支扩散的扩散:尖锐渐近性

Stochastics and Stochastic Reports Pub Date : 2004-12-01 DOI: 10.1080/10451120412331313447

A. Korostelev, O. Korosteleva

引用次数: 1

Further calculations for Israeli options 以色列选择的进一步计算

Stochastics and Stochastic Reports Pub Date : 2004-12-01 DOI: 10.1080/10451120412331313438

E. Baurdoux, A. Kyprianou

{"title":"Further calculations for Israeli options","authors":"E. Baurdoux, A. Kyprianou","doi":"10.1080/10451120412331313438","DOIUrl":"https://doi.org/10.1080/10451120412331313438","url":null,"abstract":"Recently Kifer introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment not less than the holder's claim had they exercised at that moment. Kifer shows that pricing and hedging of these options reduces to evaluating a stochastic saddle point problem associated with Dynkin games. Kyprianou, A.E. (2004) \"Some calculations for Israeli options\", Fin. Stoch. 8, 73-86 gives two examples of perpetual Israeli options where the value function and optimal strategies may be calculated explicity. In this article, we give a third example of a perpetual Israeli option where the contingent claim is based on the integral of the price process. This time the value function is shown to be the unique solution to a (two sided) free boundary value problem on (0, ∞) which is solved by taking an appropriately rescaled linear combination of Kummer functions. The probabilistic methods we appeal to in this paper centre around the interaction between the analytic boundary conditions in the free boundary problem, Itô's formula with local time and the martingale, supermartingle and submartingale properties associated with the solution to the stochastic saddle point problem.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129033802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 32

Lévy Approximation of Increment Processes with Markov Switching 马尔可夫交换下增量过程的lsamvy逼近

Stochastics and Stochastic Reports Pub Date : 2004-10-01 DOI: 10.1080/10451120412331292207

V. Korolyuk, N. Limnios

引用次数: 2

Corrigendum: Large deviations for multi-dimensional reflected fractional Brownian motion 更正:多维反射分数布朗运动的大偏差

Stochastics and Stochastic Reports Pub Date : 2004-10-01 DOI: 10.1080/10451120412331295963

K. Majewski

引用次数: 2

Measure-valued Markov processes and stochastic flows on abstract spaces 抽象空间上的测度值马尔可夫过程与随机流

Stochastics and Stochastic Reports Pub Date : 2004-10-01 DOI: 10.1080/10451120422331292216

A. Dorogovtsev

引用次数: 12

Existence and uniqueness for solutions of one dimensional SDE's driven by an additive fractional noise 加性分数噪声驱动一维SDE解的存在唯一性

Stochastics and Stochastic Reports Pub Date : 2004-10-01 DOI: 10.1080/10451120412331299336

L. Denis, M. Erraoui, Y. Ouknine

引用次数: 6

Probabilistic interpretation of a system of quasilinear parabolic PDEs 拟线性抛物型偏微分方程系统的概率解释

Stochastics and Stochastic Reports Pub Date : 2004-10-01 DOI: 10.1080/10451120412331303150

A.B. Sow *, É. Pardoux

引用次数: 17

On approximation of a class of stochastic integrals and interpolation 一类随机积分的逼近与插值

Stochastics and Stochastic Reports Pub Date : 2004-08-01 DOI: 10.1080/10451120410001728445

C. Geiss, Stefan Geiss †

引用次数: 52