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1.
Let X={X(t),t∈ℝ N } be a Gaussian random field with values in ℝ d defined by
X(t) = (X1(t), ?, Xd(t)),    t ? \mathbbRN,X(t) = (X_1(t), \ldots, X_d(t)),\quad t \in {\mathbb{R}}^N,  相似文献
2.
We introduce a weak Galerkin finite element method for the valuation of American options governed by the Black-Scholes equation. In order to implement, we need to solve the optimal exercise boundary and then introduce an artificial boundary to make the computational domain bounded. For the optimal exercise boundary, which satisfies a nonlinear Volterra integral equation, it is resolved by a higher-order collocation method based on graded meshes. With the computed optimal exercise boundary, the front-fixing technique is employed to transform the free boundary problem to a one- dimensional parabolic problem in a half infinite area. For the other spatial domain boundary, a perfectly matched layer is used to truncate the unbounded domain and carry out the computation. Finally, the resulting initial-boundary value problems are solved by weak Galerkin finite element method, and numerical examples are provided to illustrate the efficiency of the method.  相似文献
3.
We study three types of practical optimization problems faced by a firm that can control its liquid reserves by paying dividends and by issuing new equity. In the first problem, we consider the classical dividend problem without equity issuance. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of issuing new equity over strategies associated with positive reserves at all times. The third problem has the same objective as the second one, but with no constraints on the reserves. Under the assumption of proportional transaction costs, we identify the value functions and the optimal strategies. We also present the relationship between three problems.  相似文献
4.
Let B H,K = {B H,K (t), t ∈ ?+} be a bifractional Brownian motion in ? d . This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is obtained for K = 1). The exact Hausdorff measures of the image, graph and the level set of B H,K are investigated. The results extend the corresponding results proved by Talagrand and Xiao for fractional Brownian motion.  相似文献
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