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In this paper, the existence and chaos decomposition
of local time of fractional Brownian motion are studied within the canonical
framework of white noise analysis. We prove that the local time of -dimensional
fractional Brownian motion with 1-parameter is a Hida distribution through white
noise approach. Under some conditions, it exists in . Moreover, the
Wiener-Ito chaos decomposition of it is also given in terms of Hermite
polynomials. Finally, similar results of -dimensional fractional Brownian
motion with -parameter are also obtained. We popularize some results in
Bakun (2000) for the case of Brownian motion.
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In this paper, the author discusses the convergence
for weighted sums of sequences of -mixing random variables under
-th
uniform integrability, which is the same as that in the independent case.
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This paper considers the problem of maximizing expected
utility from consumption and terminal wealth under model uncertainty for a general
semimartingale market, where the agent with an initial capital and a random endowment
can invest. To find a solution to the investment problem we use the martingale method.
We first prove that under appropriate assumptions a unique solution to the investment
problem exists. Then we deduce that the value functions of primal problem and dual
problem are convex conjugate functions. Furthermore we consider a diffusion-jump-model
where the coefficients depend on the state of a Markov chain and the investor is
ambiguity to the intensity of the underlying Poisson process. Finally, for an agent
with the logarithmic utility function, we use the stochastic control method to derive
the Hamilton-Jacobi-Bellmann (HJB) equation. And the solution to this HJB equation can
be determined numerically. We also show how thereby the optimal investment strategy
can be computed.
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This paper studies the variance of blocked
cross-validation estimator of the prediction error recently proposed in the
literature. A more accuracy representation of the variance is provided and the
main theorem shows that there exists no universal (valid under all distributions)
unbiased estimator of the variance.
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In this paper, a Bernstein-polynomial-based likelihood
method is proposed for the partially linear model under monotonicity constraints.
Monotone Bernstein polynomials are employed to approximate the monotone
nonparametric function in the model. The estimator of the regression parameter
is shown to be asymptotically normal and efficient, and the rate of convergence
of the estimator of the nonparametric component is established, which could be
the optimal under the smooth assumptions. A simulation study and a real data
analysis are conducted to evaluate the finite sample performance of the proposed
method.
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This mansuscript focuses on a kind of two-dimensional
risk model with stochastic premium income and the model allows for dependence
between premiums and claims. By Laplace transforms, we prove that the model
proposed in this paper can be reduced into a kind of risk model with stochastic
premium incomes, and the premium income is independent of the claim process.
When the individual claims are the "light-tailed" case, an upper bound for
ruin probability is derived by martingale approach. When the claims belong to
a kind of heavy-tailed distribution, the asymptotic estimation for ruin
probability is given when the initial surplus tends to infinity.
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The problem of estimating the scale parameter in the
Pareto distribution from interval censored observations is considered. Four kinds of
estimators, including the maximum likelihood estimator and least square estimator,
are evaluated. The variance of them are compared, and the numerical simulation results
is also given.
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To down-weight the influence of the distributional
deviations and outliers, in this paper, we carry out robust Bayesian analysis
for general factor analytic model combined with normal scale mixture model.
Gibbs sampler is used to draw random observations from the posterior.
Statistical inferences are carried out based on the empirical distribution
of these observations. Two real data sets are analyzed to illustrate the
effectiveness of the proposed method.
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In this paper, the risk model under constant dividend
barrier strategy is studied, in which the premium income follows a compound
Poisson process and the arrival of the claims is a p-thinning process of the
premium arrival process. The integral equations with boundary conditions for
the expected discounted aggregate dividend payments and the expected discounted
penalty function until ruin are derived. In addition, the explicit expressions
for the Laplace transform of the ruin time and the expected aggregate discounted
dividend payments until ruin are given when the individual stochastic premium
amount and claim amount are exponentially distributed. Finally, the optimal
barrier is presented under the condition of maximizing the expectation of the
difference between discounted aggregate dividends until ruin and the deficit at ruin.
