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In order to improve the accuracy
of the diffusion coefficient estimation, we propose a new
combining estimator to estimate the diffusion coefficient
by dynamically integrating information from the time-domain
and the state-domain. We find that the proposed estimator
can effectively estimate the diffusion coefficient of diffusion
models, as we show in this paper on simulated time series.
Under certain conditions, the asymptotic normality is separately
established for the proposed nonparametric estimators and the
proposed theorem proves that the time-domain and state-domain
estimators are asymptotically independent. Extensive simulations
demonstrate the proposed estimator outperforms the other two
estimators, and also outperforms the ones in the literature.
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Generalized operators of white noise play a very important
role in the theory and application of white noise analysis. In the present thesis,
we mainly discuss the integration of generalized operator-valued functions with
respect to generalized operator-valued measures and related topics. The main work
is as follows: First, a notion of generalized operator-valued measures is introduced,
and variations of such a measure are investigated in the sense of symbol and operator p-norm, respectively.
Secondly, an integral, called Bochner-Wick integral, of a generalized operator valued function with respect to
a generalized operator valued measure is defined. Properties of the integral are examined and corresponding
convergence theorems are established. Finally, the Fubini theorem for the integral
is discussed and applications are shown.
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In this paper, the pricing problem of CDS with the interest
rate risk and contagious risk is investigated. The interest rate satisfies the fractional
Vasicek interest rate model. We model the firm's default intensity. We derive the pricing
formula of risky bonds when the default is correlated with interest rate and get the
price of CDS.
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We assume that there exist two kinds of investors in
the market, the first kind investors, have the market information ,
which is given by a -dimensional Brownian motion
as
well as an integer-valued random measure . The second
kind, however, have the information from the progressive enlargement
filtration of by the default time
modeled by the so called
the generalized Cox model. We characterize this model with a triplet and describe
main properties such as the survival process and the conditional density of
. The
-decomposition of a
-martingale is not
trivial in contrast to the class Cox model.
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In this paper, we consider a discrete-time process
driven by general reinsurance and an interest rate process. The rate of
interest is assumed to have a dependent autoregressive structure. We obtain
the recursive and integral equations for ruin probability, and the upper
bound of ruin probability is given with recursive method. The results were
applied to the proportional reinsurance and excess of loss treaty. To
illustrate these results, some numerical examples are included.
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Let be a sequence of pairwise
negatively quadrant dependent random variables with and let
be a sequence of strictly increasing convex numbers. In
this paper, the Feller (1946)'s work on independent identically distributed
variables with infinite expectation is extended to the case of pairwise negative
quadrant dependence random variables.
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Growth curve model has broad application background,
and plays an important role in some fields such as economics, biology, medical
research. Many of existing estimation of its parameter matrix have been
obtained based on the least squares method or maximum likelihood method.
When distribution of the error term is partial peak, or heavy tail, or there
exist outliers, estimation obtained by least square method will be invalid.
The distribution of the error must be known in maximum likelihood estimation,
which is often not satisfied. Quantile regression method can compensate for
these defects and the estimation has good robustness. In this paper, quantile
regression is used to give the estimation of growth curve model, and its
asymptotic normality.
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In this paper, the best linear unbiased estimator of
regression coefficients in the linear model is studied. Under weighted balanced
loss function the minimum risk properties of linear estimator of regression
coefficients in the class of linear unbiased estimator is discussed. Furthermore,
some kinds of relative efficiencies of the best linear unbiased estimator and
ordinary least squares estimator are given, and the lower bound or upper bound
of these relative efficiencies are also given.
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In this paper, under -mixing random variables,
we discuss the uniformly asymptotic normality of the quantile estimate and
give its rate. The rate of normal approximation is shown as ,
under some certain conditions. The result can apply to the VaR quantile
estimator.
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This paper is concerned with the optimal portfolio choice
of an investor under the inflation and rare events impact, where the investor is
aversive not only to the risk of loss but also to model uncertainty. An investor
allocates his assets to the risky asset and the riskless asset. First, we obtain
the dynamics of consumer-basket-price with inflation by using formula. Second,
under maximizing the expected utility of intermediate consumption and terminal
wealth discounted by inflation, the value function of ambiguity aversion investors
is characterized. Through the dynamic programming principle, we derive the HJB
equation satisfied by the value function of an investor's optimal consumption and
portfolio. Third, applying market decomposition method to solving the HJB equation,
the optimal consumption and portfolio policy for investors is obtained. Finally,
the effect of the ambiguity aversion, risk aversion and inflation on an investor's
optimal allocation strategy is analyzed by numerical simulation.
