9,319 research outputs found
Alternative approach to derive q-potential measures of refracted spectrally L\'evy processes
For a refracted L\'evy process driven by a spectrally negative L\'evy
process, we use a different approach to derive expressions for its q-potential
measures without killing. Unlike previous methods whose derivations depend on
scale functions which are defined only for spectrally negative L\'evy
processes, our approach is free of scale functions. This makes it possible to
extend the result here to a quite general refracted L\'evy process by applying
the approach presented below
Pricing variable annuities with multi-layer expense strategy
We study the problem of pricing variable annuities with a multi-layer expense
strategy, under which the insurer charges fees from the policyholder's account
only when the account value lies in some pre-specified disjoint intervals,
where on each pre-specified interval, the fee rate is fixed and can be
different from that on other interval. We model the asset that is the
underlying fund of the variable annuity by a hyper-exponential jump diffusion
process. Theoretically, for a jump diffusion process with hyper-exponential
jumps and three-valued drift, we obtain expressions for the Laplace transforms
of its distribution and its occupation times, i.e., the time that it spends
below or above a pre-specified level. With these results, we derive closed-form
formulas to determine the fair fee rate. Moreover, the total fees that will be
collected by the insurer and the total time of deducting fees are also
computed. In addition, some numerical examples are presented to illustrate our
results
Occupation times of generalized Ornstein-Uhlenbeck processes with two-sided exponential jumps
For an Ornstein-Uhlenbeck process driven by a double exponential jump
diffusion process, we obtain formulas for the joint Laplace transform of it and
its occupation times. The approach used is remarkable and can be extended to
investigate the occupation times of an Ornstein-Uhlenbeck process driven by a
more general Levy process
The distribution of refracted L\'evy processes with jumps having rational Laplace transforms
We consider a refracted jump diffusion process having two-sided jumps with
rational Laplace transforms. For such a process, by applying a straightforward
but interesting approach, we derive formulas for the Laplace transform of its
distribution. Our formulas are presented in an attractive form and the approach
is novel. In particular, the idea in the application of an approximating
procedure is remarkable. Besides, the results are used to price Variable
Annuities with state-dependent fees
Occupation times of refracted Levy processes with jumps having rational Laplace transforms
We investigate a refracted Levy process driven by a jump diffusion process,
whose jumps have rational Laplace transforms. For such a stochastic process,
formulas for the Laplace transform of its occupation times are deduced. To
derive the main results, some modifications on our previous approach have been
made. In addition, we obtain a very interesting identity, which is conjectured
to hold for a general refracted Levy process
A note on refracted L\'evy processes without positive jumps
For a refracted spectrally negative Levy process, we find some new and
fantastic formulas for its q-potential measures without killing. Unlike
previous results, which are written in terms of the known q-scale functions,
our formulas are free of the q-scale functions. This makes our results become
extremely important since it is likely that our formulas also hold for a
general refracted Levy process
Stochastic continuity, irreducibility and non confluence for SDEs with jumps
In this paper, we investigate stochastic continuity (with respect to the
initial value), irreducibility and non confluence property of the solutions of
stochastic differential equations with jumps. The conditions we posed are
weaker than those relevant conditions existing in the literature. We also
provide an example to support our new conditions.Comment: 16 page
New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients
The object of the present paper is to find new sufficient conditions for the
existence of unique strong solutions to a class of (time-inhomogeneous)
stochastic differential equations with random, non-Lipschitzian coefficients.
We give an example to show that our conditions are indeed weaker than those
relevant conditions existing in the literature. We also derive moment
estimations for the maximum process of the solution. Finally, we present a
sufficient condition to ensure the non confluence property of the solution of
time-homogeneous SDE which, in one dimension, is nothing but stochastic
monotone property of the solution.Comment: 21 page
Tracking multiple moving objects in images using Markov Chain Monte Carlo
A new Bayesian state and parameter learning algorithm for multiple target
tracking (MTT) models with image observations is proposed. Specifically, a
Markov chain Monte Carlo algorithm is designed to sample from the posterior
distribution of the unknown number of targets, their birth and death times,
states and model parameters, which constitutes the complete solution to the
tracking problem. The conventional approach is to pre-process the images to
extract point observations and then perform tracking. We model the image
generation process directly to avoid potential loss of information when
extracting point observations. Numerical examples show that our algorithm has
improved tracking performance over commonly used techniques, for both synthetic
examples and real florescent microscopy data, especially in the case of dim
targets with overlapping illuminated regions
Occupation times of general L\'evy processes
For an arbitrary L\'evy process which is not a compound Poisson process,
we are interested in its occupation times. We use a quite novel and useful
approach to derive formulas for the Laplace transform of the joint distribution
of and its occupation times. Our formulas are compact, and more
importantly, the forms of the formulas clearly demonstrate the essential
quantities for the calculation of occupation times of . It is believed that
our results are important not only for the study of stochastic processes, but
also for financial applications
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