Filters

2006 - 200912010 - 20203

More filters

2019 - 201932020 - 20211
Reset filters

Settings

Author: Belomestny, Denis × Subject: optimal stopping ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm
    (Oxford [u.a.] : Wiley-Blackwell, 2020) Belomestny, Denis; Kaledin, Maxim; Schoenmakers, John
    In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete-time case the WSM algorithm leads to semitractability of the corresponding optimal stopping problem in the sense that its complexity is bounded in order by (Formula presented.) with (Formula presented.) being the dimension of the underlying Markov chain. Furthermore, we study the WSM approach in the context of continuous-time optimal stopping problems and derive the corresponding complexity bounds. Although we cannot prove semitractability in this case, our bounds turn out to be the tightest ones among the complexity bounds known in the literature. We illustrate our theoretical findings by a numerical example. © 2020 Wiley Periodicals LLC
  • Thumbnail Image
    Item
    Regression on particle systems connected to mean-field SDEs with applications
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Belomestny, Denis; Schoenmakers, John G.M.
    In this note we consider the problem of using regression on interacting particles to compute conditional expectations for McKean-Vlasov SDEs. We prove general result on convergence of linear regression algorithms and establish the corresponding rates of convergence. Application to optimal stopping and variance reduction are considered.
  • Thumbnail Image
    Item
    On the rates of convergence of simulation based optimization algorithms for optimal stopping problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Belomestny, Denis
    In this paper we study simulation-based optimization algorithms for solving discrete time optimal stopping problems. Using large deviation theory for the increments of empirical processes, we derive optimal convergence rates for the value function estimate and show that they can not be improved in general. The rates derived provide a guide to the choice of the number of simulated paths needed in optimization step, which is crucial for the good performance of any simulation-based optimization algorithm. Finally, we present a numerical example of solving optimal stopping problem arising in finance that illustrates our theoretical findings
  • Thumbnail Image
    Item
    An iteration procedure for solving integral equations related to the American put options
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Belomestny, Denis; Gapeev, Pavel
    A new algorithm for pricing American put option in the Black-Scholes model is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation converges in a finite number of steps and delivers in each step a lower or an upper bound for the price of discretized option on the whole time interval. The method developed can be easily implemented and carried over to the case of more general optimal stopping problems.