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In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDEs), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDEs). As some applications, a general converse comparison theorem for RBSDEs is obtained and some properties of RBSDEs are discussed.
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We generalize the framework of [18] for optimal stopping time problem to allow a certain restricted class of stopping times. By using classical results in probability theory on families of random variables indexed by a restricted family of stopping times, we prove the existence of an optimal time, give characterizations of the minimal and maximal optimal stopping times, and provide some local properties of the value function family, in concert with all special cases studied previously.
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In this paper, we discuss tail asymptoticsproperties for a class of infinite phase type distributions based onprobability generating function or Laplace-Stieltjes transform. The results show that, unlike finite phase cases, the tail asymptotics for the infinite phase type distributions we considered do not decay
geometrically or exponentially.
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In this paper, we study the stochastic comparisons of order statistics from generalized normal distributions. We obtain some sufficient conditions for ordering results based on parameter matrix and vector majorization comparisons. These conditions are necessary in some cases.
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In this paper, we consider the ultra-high dimensional partially linear model, where the dimensionality p of linear component is much larger than the sample size n, and p can be as large as an exponential of the sample size n. Firstly, we transform the ultra-high dimensional partially linear model into the ultra-high dimensional linear model based the profile technique used in the semiparametric regression. Secondly, in order to finish the variable screening for high-dimensional linear component, we propose a variable screening method called as the profile greedy forward regression (PGFR) by combining the greedy algorithm with the forward regression (FR) method. The proposed PGFR method not only considers the correlation between the covariates, but also identifies all relevant predictors consistently and possesses the screening consistency property under the some regularity conditions. We further propose the BIC criterion to determine whether the selected model contains the true model with probability tending to one. Finally, some simulation studies and a real application are conducted to examine the finite sample performance of the proposed PGFR procedure.
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This paper assumes that company's asset process follows a non-linear model, which reflects the relationship between the operation costs and the size business. Suppose that the company can control the asset process by changing the size of business, paying dividends and raising money dynamically. Meanwhile, it bears both fixed and proportional transaction costs during the control processes. Under the objective of maximizing the company's value, we obtain the explicit solutions of optimal strategies and value function by using the optimal control method. The results illustrate that the optimal strategies depend on the parameters of the model. The company should expand the business scale with the increasing of asset. Dividends should be paid out according to the impulse control
strategy. Financing is profitable to avoid bankruptcy if and only if the transaction costs are relatively low.
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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q<p<\infty and large t. Explicit and sharp formulas for c(t) are also given.
