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In this paper, we consider the speed of convergence of the threshold
version of bipower variation for a semimartingale, which is driven by a standard Brownian
motion and a pure jump Levy process with possibly infinite activity of the small jumps.
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Bridge regression, a special family of penalized regressions
of a penalty function with
, has been studied in many
literatures. In this paper, we provide some theoretical results of how the shrinkage
rule changing with under two settings:
and
,
respectively. Simulation results are conducted to evaluate the performance of the
proposed method.
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In this paper, it is assumed that the underlying is a Markov
skeleton process (abbreviated MSP): this process can be better reflecting the instability
of the financial market. Using the properties of Markov skeleton process, the characteristic
function of the price process is given, combined with fast Fourier transform (FFT) method,
the pricing formula of derivatives under the Markov skeleton process is given. The results
of this paper can be applied to price other financial derivatives, and it enriching the
pricing theory of financial derivatives.
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The periods of states for Markov chains in a random environment
are introduced and some properties about periods are investigated. An open problem
(Orey, 1991; Problem 1.3.3) is studied under the assumption that states have periods.
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This study has considered the compound Poisson risk model
perturbed by diffusion with constant interest and obtained an integral-differential
equation for the Gerber-Shiu discounted penalty function. Asymptotic expression for
the ultimate ruin probability also derived across the study.
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In this paper, the concept of renewal-geometry process is put
forward based on the idea of stage deterioration of system. The definitions of
renewal-geometry function, the quasi renewal-geometry age and quasi residual
renewal-geometry life for the new stochastic process are given. The related properties
of renewal-geometry process are studied. Finally, the related theory results are
simulated by an example.
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In this paper, we present an approach of changing probability
measures associated with numeraire changes to the pricing of catastrophe event (CAT) derivatives.
We assume that the underlying asset and a discounted zero-coupon bond follow
a stochastic process, respectively. We obtain explicit closed form formulae that permit
the interest rate to be random. We shall see that sometimes it is convenient to change
the numeraire because of modeling considerations as well. Furthermore, we show that,
for compound Poisson losses, sometimes a continuum of jump sizes can be replaced by
finitely many jump sizes. Therefore, sometimes we can explore further applications of
the closed-form formulae beyond the case that the compound Poisson losses are finitely
many jump sizes. Finally, numerical experiments demonstrate how financial risks and
catastrophic risks affect the price of double trigger put option.
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The supermarket model has been an important mathematical tool
in the study of resource management in large-scale networks by means of some advantages,
such as, simple operations, quick reaction, real-time management and control and so on.
It is widely applied in internet of things, cloud computing, cloud manufacturing, big
data, transportation, health care and other important practical fields. Up to now,
analysis of the asymmetric supermarket models is an increasingly interesting topic in
this area.
In this paper, we analyze an asymmetric supermarket model. Because the M
servers are different from each other, the routine selection policies of each customer
become to have a complex structure, where not only are the routine selection policies
related to the different queue lengths and the different service speeds among the M
servers, but they are also related to the customer's preference for the M servers.
For this, we set up several useful routine selection policies in terms of the
decision-making methods. Based on this, we provide the Markov reward processes of the
asymmetric supermarket model and establish the associated functional reward equations,
give a useful value iterative algorithm for solving the functional reward equations,
obtain a criterion of performance evaluation in the asymmetric supermarket model through
a double-direction optimization, and show that the sequence of iterative reward functions
is monotone and the value iterative algorithm is convergent. This paper provides new
and useful highlight on understanding how the asymmetric supermarket model is applied
to resource management and control in large-scale networks both from the objective
conditions and from the subjective behavior. At the same time, the methodology and main
results of this paper give some basic theory and techniques in the study of asymmetric
supermarket models for the first time.
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The covariate-adjusted regression model was initially proposed for
the situations where both the predictors and the response variables are not directly observed,
but are distorted by some common observable covariates. In this paper, we investigate a
covariate-adjusted nonparametric regression (CANR) model and consider the proposed model on
time series setting. We develop a two-step estimation procedure to estimate the regression
function. The asymptotic property of the proposed estimation is investigated under the
-mixing conditions. Both the real data and simulated examples are provided for
illustration.
