7,132 research outputs found
On the Exact Simulation of (Jump) Diffusion Bridges
In this paper we outline methodology to efficiently simulate (jump) diffusion
bridge sample paths without discretisation error. We achieve this by
considering the simulation of conditioned (jump) diffusion bridge sample paths
in light of recent work developing a mathematical framework for simulating
finite dimensional sample path skeletons (which flexibly characterise the
entirety of sample paths).Comment: 12 pages, 3 figure
Small-time asymptotics of stopped L\'evy bridges and simulation schemes with controlled bias
We characterize the small-time asymptotic behavior of the exit probability of
a L\'evy process out of a two-sided interval and of the law of its overshoot,
conditionally on the terminal value of the process. The asymptotic expansions
are given in the form of a first-order term and a precise computable error
bound. As an important application of these formulas, we develop a novel
adaptive discretization scheme for the Monte Carlo computation of functionals
of killed L\'evy processes with controlled bias. The considered functionals
appear in several domains of mathematical finance (e.g., structural credit risk
models, pricing of barrier options, and contingent convertible bonds) as well
as in natural sciences. The proposed algorithm works by adding discretization
points sampled from the L\'evy bridge density to the skeleton of the process
until the overall error for a given trajectory becomes smaller than the maximum
tolerance given by the user.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ517 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Nonparametric Bayesian methods for one-dimensional diffusion models
In this paper we review recently developed methods for nonparametric Bayesian
inference for one-dimensional diffusion models. We discuss different possible
prior distributions, computational issues, and asymptotic results
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