This paper considers a first passage model for discounted semi-Markov decision processes with denumerable states and nonnegative costs. The criterion to be optimized is the expected discounted cost incurred during a first passage time to a given target set. We first construct a semi-Markov decision process under a given semi-Markov decision kernel and a policy. Then, we prove that the value function satisfies the optimality equation and there exists an optimal (or ε-optimal) stationary policy under suitable conditions by using a minimum nonnegative solution approach. Further we give some properties of optimal policies. In addition, a value iteration algorithm for computing the value function and optimal policies is developed and an example is given. Finally, it is showed that our model is an extension of the first passage models for both discrete-time and continuous-time Markov decision processes.
A class of piecewise smooth functions in R^{2} is considered. The propagation law of the Radon transform of the function is derived. The singularities inversion formula of the Radon transform is derived from the propagation law. The examples of singularities and singularities inversion of the Radon transform are given.
In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d. heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV (extended regular variation). Lundberg type limiting results on the finite time ruin probabilities are also investigated.
In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.
Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″(t) + g(t)f(t, u(t)) = 0, 0 < t < 1, u(0) = u(1) = ∫_{0}^{1}m(s)u(s)ds, where m ∈ L^{1}[0, 1], g : (0, 1) → [0,∞) is continuous, symmetric on (0, 1) and maybe singular at t = 0 and t = 1, f : [0, 1] × [0,∞) → [0,∞) is continuous and f(·, x) is symmetric on [0, 1] for all x ∈ [0,∞).
This paper studies the least absolute deviation estimation of the high frequency financial autoregressive conditional duration (ACD) model. The asymptotic properties of the estimator are studied given mild regularity conditions. Furthermore, we develop a Wald test statistic for the linear restriction on the parameters. A simulation study is conducted for the finite sample properties of our estimator. Finally, we give an empirical study of financial duration.
This paper provides a new approach to study the solutions of a class of generalized Jacobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n + 1. A new class of generalized differential operators is defined. We investigate the kernel of the corresponding maximal operators by applying operator theory. It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic, in which there are n dimension solutions with exponential-decaying amplitude.
Surface reconstruction from scattered data is an important problem in such areas as reverse engineering and computer aided design. In solving partial differential equations derived from surface reconstruction problems, level-set method has been successfully used. We present in this paper a theoretical analysis on the existence and uniqueness of the solution of a partial differential equation derived from a model of surface reconstruction using the level-set approach. We give the uniqueness analysis of the classical solution. Results on the existence and uniqueness of the viscosity solution are also established.
This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result we obtain extends the corresponding result of Wang and Tang^{[7]} .
Consider the linear matrix equation A^{T}XA + B^{T}Y B = D, where A,B are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples.
In this paper, the existence of global attractor for 3-D complex Ginzburg Landau equation is considered. By a decomposition of solution operator, it is shown that the global attractor Ai in H^{i}(Ω) is actually equal to a global attractor Ai in H^{i}(Ω) (i ≠ j, i, j = 1, 2, · · ·m).
In this paper, the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind. Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity. Moreover, the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional L. Subsequently, the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate. Finally, we give the numerical results to verify the feasibility of the Uzawa algorithm.
A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.
In this paper, we investigate the asymptotic behavior for the finite- and infinite-time ruin probabilities of a nonstandard renewal model in which the claims are identically distributed but not necessarily independent. Under the assumptions that the identical distribution of the claims belongs to the class of extended regular variation (ERV) and that the tails of joint distributions of every two claims are negligible compared to the tails of their margins, we obtain the precise approximations for the finite- and infinite-time ruin probabilities.
In this paper, we adopt the robust optimization method to consider linear complementarity problems in which the data is not specified exactly or is uncertain, and it is only known to belong to a prescribed uncertainty set. We propose the notion of the ρ - robust counterpart and the ρ - robust solution of uncertain linear complementarity problems. We discuss uncertain linear complementarity problems with three different uncertainty sets, respectively, including an unknown-but-bounded uncertainty set, an ellipsoidal uncertainty set and an intersection-of-ellipsoids uncertainty set, and present some sufficient and necessary (or sufficient) conditions which ρ - robust solutions satisfy. Some special cases are investigated in this paper.