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20051020BuchA Note on Optimal Stopping in Models with Delay Gapeev, Pavel V.; Reiß, MarkusWe consider an optimal stopping problem in a certain model described by a stochastic delay differential equation. We reduce the initial problem to a freeboundary problem of parabolic type and prove the corresponding ...

20060517DiskussionspapierAn Iteration Procedure for Solving Integral Equations Related to Optimal Stopping Problems Belomestny, Denis; Gapeev, Pavel V.A new algorithm for finding value functions of finite horizon optimal stopping problems in onedimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The ...

20050210DiskussionspapierAn Optimal Stopping Problem in a DiffusionType Model with Delay Gapeev, Pavel V.; Reiß, MarkusWe present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem ...

20060911DiskussionspapierDiscounted Optimal Stopping for Maxima in Diffusion Models with Finite Horizon Gapeev, Pavel V.We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with ...

20060911DiskussionspapierDiscounted Optimal Stopping for Maxima of some JumpDiffusion Processes Gapeev, Pavel V.We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing ...

20060911DiskussionspapierIntegral Options in Models with Jumps Gapeev, Pavel V.We present an explicit solution to the formulated in [17] optimal stopping problem for a geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an ...

20061024DiskussionspapierMultiple Disorder Problems for Wiener and Compound Poisson Processes With Exponential Jumps Gapeev, Pavel V.The multiple disorder problem consists of finding a sequence of stoppingtimes which are as close as possible to the (unknown) times of ``disorder´´when the distribution of an observed process changes its probability ...

20051020BuchOn Large Deviations in Testing OrnsteinUhlenbeck Type Models with Delay Gapeev, Pavel V.; Küchler, UweWe obtain an explicit form of fine large deviation theorems for the loglikelihood ratio in testing models with observed OrnsteinUhlenbeck processes and get explicit rates of decrease for error probabilities of NeymanPearson, ...

20051020BuchOn Markovian Short Rates in Term Structure Models Driven by JumpDiffusion Processes Gapeev, Pavel V.; Küchler, UweWe study a bond market model and related term structure of interest rates where prices of zero coupon bonds are driven by a jumpdiffusion process. We present a criterion on the deterministic forward rate volatilities under ...

20060911DiskussionspapierOn Maximal Inequalities for some Jump Processes Gapeev, Pavel V.We present a solution to the considered in [5] and [22] optimal stopping problem for some jump processes. The method of proof is based on reducing the initial problem to an integrodifferential freeboundary problem where ...

20060911DiskussionspapierPerpetual Barrier Options in JumpDiffusion Models Gapeev, Pavel V.We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on ...