Volume 17, Issue 2

In the area of financial mathematics Monte Carlo simulation is often successfully used to estimate the prices of certain products. However in many cases calibrating Monte Carlo based models to market prices turns out to be difficult due to stochastic noise arising in the objective functionals. This noise can be reduced by the use of fixed point-sets of random numbers which are reused for every new set of parameters (i.e. in every new step of the optimization algorithm used for calibration). In this paper we argue that the above technique can be enhanced by using fixed low discrepancy point-sets (quasi-Monte Carlo method) instead of ones originating from Pseudo-Random-Number generators. The method is applied to two different financial models and the results are compared with the classical one.

This paper presents a hybrid model (stochastic/deterministic) that describes the time evolution of chemical species in a homogenous gas-phase combustion reaction process at constant volume. First, the paper briefly introduces currently employed stochastic algorithms. Next, the development of the hybrid algorithm is detailed. The model is then validated and tested using a reduced reaction mechanism for methane combustion. The effect of user-input performance parameters on stochastic behavior and computational time is studied. The computational time of the algorithm compared to the stochastic simulation algorithm is then compared, and finally, the effect of multiple runs on auto-ignition time is investigated.

This paper is devoted to the accuracy and reliability estimation (in uniform metrics) of calculation of improper integrals depending on a parameter t , using the Monte Carlo method. For this, estimates for the probability of deviation in the uniform metric of sums of independent identically distributed fields, which belong to Orlicz spaces, were found.

Using a high performance computer cluster, we run simulations regarding an open problem about d -dimensional critical branching random walks in a random IID environment The environment is given by the rule that at every site independently, with probability p ∈ [0, 1], there is a cookie , completely suppressing the branching of any particle located there. The simulations suggest self averaging : the asymptotic survival probability in n steps is the same in the annealed and the quenched case; it is , where q ≔ 1 – p . This particular asymptotics indicates a non-trivial phenomenon: the tail of the survival probability (both in the annealed and the quenched case) is the same as in the case of non-spatial unit time critical branching, where the branching rule is modified: branching only takes place with probability q for every particle at every iteration.