21,556 research outputs found
Multilevel Monte Carlo methods for applications in finance
Since Giles introduced the multilevel Monte Carlo path simulation method
[18], there has been rapid development of the technique for a variety of
applications in computational finance. This paper surveys the progress so far,
highlights the key features in achieving a high rate of multilevel variance
convergence, and suggests directions for future research.Comment: arXiv admin note: text overlap with arXiv:1202.6283; and with
arXiv:1106.4730 by other author
A numerical study of radial basis function based methods for option pricing under one dimension jump-diffusion model
The aim of this paper is to show how option prices in the Jump-diffusion model can be computed using meshless methods based on Radial Basis Function (RBF) interpolation. The RBF technique is demonstrated by solving the partial integro-differential equation (PIDE) in one-dimension for the Ameri-
can put and the European vanilla call/put options on dividend-paying stocks in the Merton and Kou Jump-diffusion models. The radial basis function we select is the Cubic Spline. We also propose a simple numerical algorithm for
finding a finite computational range of a global integral term in the PIDE so that the accuracy of approximation of the integral can be improved. Moreover, the solution functions of the PIDE are approximated explicitly by RBFs
which have exact forms so we can easily compute the global intergal by any kind of numerical quadrature. Finally, we will also show numerically that our scheme is second order accurate in spatial variables in both American and European cases
MCMC inference for Markov Jump Processes via the Linear Noise Approximation
Bayesian analysis for Markov jump processes is a non-trivial and challenging
problem. Although exact inference is theoretically possible, it is
computationally demanding thus its applicability is limited to a small class of
problems. In this paper we describe the application of Riemann manifold MCMC
methods using an approximation to the likelihood of the Markov jump process
which is valid when the system modelled is near its thermodynamic limit. The
proposed approach is both statistically and computationally efficient while the
convergence rate and mixing of the chains allows for fast MCMC inference. The
methodology is evaluated using numerical simulations on two problems from
chemical kinetics and one from systems biology
Robustness and epistasis in mutation-selection models
We investigate the fitness advantage associated with the robustness of a
phenotype against deleterious mutations using deterministic mutation-selection
models of quasispecies type equipped with a mesa shaped fitness landscape. We
obtain analytic results for the robustness effect which become exact in the
limit of infinite sequence length. Thereby, we are able to clarify a seeming
contradiction between recent rigorous work and an earlier heuristic treatment
based on a mapping to a Schr\"odinger equation. We exploit the quantum
mechanical analogy to calculate a correction term for finite sequence lengths
and verify our analytic results by numerical studies. In addition, we
investigate the occurrence of an error threshold for a general class of
epistatic landscape and show that diminishing epistasis is a necessary but not
sufficient condition for error threshold behavior.Comment: 20 pages, 14 figure
Bayesian Model Selection for Beta Autoregressive Processes
We deal with Bayesian inference for Beta autoregressive processes. We
restrict our attention to the class of conditionally linear processes. These
processes are particularly suitable for forecasting purposes, but are difficult
to estimate due to the constraints on the parameter space. We provide a full
Bayesian approach to the estimation and include the parameter restrictions in
the inference problem by a suitable specification of the prior distributions.
Moreover in a Bayesian framework parameter estimation and model choice can be
solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo
(MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and
solve the model selection problem following a reversible jump MCMC approach
Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory
The mean field (MF) approximation for the pion matter, being equivalent to
the leading ChPT order, involves no dynamical loops and, if self-consistent,
produces finite renormalizations only. The weight factor of the Haar measure of
the pion fields, entering the path integral, generates an effective Lagrangian
which is generally singular in the continuum limit.
There exists one parameterization of the pion fields only, for which the weight
factor is equal to unity and , respectively. This
unique parameterization ensures selfconsistency of the MF approximation. We use
it to calculate thermal Green functions of the pion gas in the MF approximation
as a power series over the temperature. The Borel transforms of thermal
averages of a function of the pion
fields with respect to the scalar pion density are found to be
. The perturbation series over the scalar
pion density for basic characteristics of the pion matter such as the pion
propagator, the pion optical potential, the scalar quark condensate
, the in-medium pion decay constant , and the
equation of state of pion matter appear to be asymptotic ones. These series are
summed up using the contour-improved Borel resummation method. The quark scalar
condensate decreases smoothly until MeV. The temperature
is the maximum temperature admissible for thermalized non-linear
sigma model at zero pion chemical potentials. The estimate of is
above the chemical freeze-out temperature MeV at RHIC and above
the phase transition to two-flavor quark matter MeV,
predicted by lattice gauge theories.Comment: Replaced with revised and extended version. Results are compared to
lattice gauge theories. 16 pages REVTeX, 13 eps figure
- …