Denis Belomestny

Duality for Multiple Stopping

In this chapter we will generalize the dual methodology presented in the previous chapter to the so called multiple stopping problems. The presentation is based on [34, 102], where also further details can be found.

Pricing Bermudan Options via Consumption Processes

In this chapter we present an alternative approach of constructing upper bounds for the values of discrete time optimal stopping problems based on consumption processes.

Dual Methods for General Optimal Control

In this chapter we extend the duality approach to general optimal control problems. The content of this chapter is based on works [35] and [62].

Dual Monte Carlo Algorithms for Optimal Control

In this chapter we discuss several non-nested dual Monte Carlo algorithms for optimal control problems.

Duality for Optimal Stopping

In this chapter we discuss basic concepts of duality for discrete time optimal stopping problems. In particular additive and multiplicative dual representations are given and their stability is discussed.

Dual Monte Carlo Algorithms for Optimal Stopping

In this chapter several non-nested dual Monte Carlo algorithms for optimal stopping problem are presented.

Simulation Based Option Pricing

Here we develop an approach for efficient pricing discrete-time American and Bermudan options which employs the fact that such options are equivalent to the European ones with a consumption, combined with analysis of the market model over a small number of steps ahead. This approach allows constructing both upper and lower bounds for the true price by Monte Carlo simulations. An adaptive choice of local lower bounds and use of the kernel interpolation technique enhance efficiency of the whole procedure, which is supported by numerical experiments.

A stochastic volatility Libor model and its robust calibration

In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration procedure which takes into account a given local correlation structure is presented. The calibration algorithm is FFT based, so fast and easy to implement.