We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which posses an intrinsic stationarity and therefore...

The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming...

In this paper, we suggest several improvements to the numerical implementation of the quantization method for stochastic control problems in order to obtain fast and accurate premium estimations. This technique is applied to derivative pricing in energy markets. Several ways of modeling energy...

Summury For a probability measure P on R d and n ∊ N consider e n = inf ∫ min a∊α V (|| x − a ||) dP ( x ) where the infimum is taken over all subsets α of R d with card(α) ≤ n and V is a nondecreasing function. Under certain conditions on V , we derive the precise n -asymptotics of...

In some recent papers, some procedures based on some weighted empirical measures related to decreasing-step Euler schemes have been investigated to approximate the stationary regime of a diffusion (possibly with jumps) for a class of functionals of the process. This method is efficient but needs...

In the paper Bally and Pagès (2000) an algorithm based on an optimal discrete quantization tree is designed to compute the solution of multi-dimensional obstacle problems for homogeneous -valued Markov chains (Xk)0[less-than-or-equals, slant]k[less-than-or-equals, slant]n. This tree is made up...

This paper shows that the 2-neighbour Kohonen algorithm is self-organizing under pretty general assumptions on the stimuli distribution [mu] (supp([mu]c) contains a non-empty open set) and is a.s. convergent--in a weakened sense--as soon as [mu] admits a log-concave density. The 0-neighbour...

In this paper we investigate a class of swing options with firm constraints in view of the modeling of supply agreements. We show, for a fully general payoff process, that the premium, solution to a stochastic control problem, is concave and piecewise affine as a function of the global...