线性离散零和问题的改进滚动时域控制

提出一种改进的滚动时域控制算法来解决离散线性时不变系统的零和问题.与普通滚动时域控制不同的是,每一步中性能指标的终端权值矩阵将随着运算的进行不断更新,这等价于延长了时域长度.严格证明了该算法得到的控制律将收敛到无限零和问题的解,同时保证了闭环系统的一致最终指数稳定性,而不需要对终端状态、时域长度及终端性能指标施加额外的约束.最后仿真例子说明了该算法的有效性.     

Risk-sensitive finite-horizon piecewise deterministic Markov decision processes

This paper deals with risk-sensitive piecewise deterministic Markov decision processes, where the expected exponential utility of a finite-horizon reward is to be maximized. Both the transition rates and reward functions are allowed to be unbounded. Feynman–Kac’s formula is developed in our setup, using which along with an approximation technique, we establish the associated Hamilton–Jacobi–Bellman equation and the existence of risk-sensitive optimal policies under suitable conditions.     

A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.     

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.     

Limit of the solutions for the finite horizon problems as the optimal solution to the infinite horizon optimization problems

In this paper, we consider how to construct the optimal solutions for the undiscounted discrete time infinite horizon optimization problems. We present the conditions under which the limit of the solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problem under two modified overtaking criteria, as well as the conditions under which it is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of a simple one-sector growth model to examine the impacts of discounting on the optimal path.     

Discrete-Time BSDEs with Random Terminal Horizon

This article studies the theory of discrete-time backward stochastic differential equations (also called BSDEs) with a random terminal time, which is not a stopping time. We follow Cohen and Elliott [2 Cohen , S.N. , and Elliott , R.J. 2010 . A general theory of finite state backward stochastic difference equations . Stochastic Processes and Their Applications 120 ( 4 ): 442 – 466 .[Crossref], [Web of Science ®] , [Google Scholar]] and consider a reference filtration generated by a general discrete-time finite-state process. The martingale representation theorem for essentially bounded martingales under progressively enlarged filtration is established. Then we prove the existence and uniqueness theorem of BSDEs under enlarged filtration using some weak assumptions of the driver. We also present conditions for a comparison theorem. Applications to nonlinear expectations and optimal design of dynamic default risk are explored.     

The quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

Using a new tortoise coordinate transformation,we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time,and obtain the event horizon surface gravity and the Hawking temperature on that event horizon.The results show that there is a crossing of particle energy near the event horizon.We derive the maximum overlap of the positive and negative energy levels.It is also found that the Hawking temperature of a black hole depends not only on the time,but also on the angle.There is a problem of dimension in the usual tortoise coordinate,so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.     

Solving a finite horizon EPQ problem with backorders

This paper presents an alternative approach to solve a finite horizon production lot sizing model with backorders using Cauchy-Bunyakovsky-Schwarz Inequality. The optimal batch size is derived from a sequence number of batches. We prove that a constant batch size policy with one fill rate is better than the variable batch sizes with variable fill rates. Finally, a practical approach is proposed to find the optimal solutions for a discrete planning horizon and discrete batch sizes.     

Optimal bond portfolios with fixed time to maturity

We study interest rate models where the term structure is given by an affine relation and in particular where the driving stochastic processes are so-called generalized Ornstein–Uhlenbeck processes.     

K-N-K黑洞视界极点处二级无限小邻域的度规

利用极限法得到了Kerr-Newman-Kasuya(K-N-K)黑洞视界极点处二级无限小邻域的度规,并证明这个时空度规是以常角速度转动的 Rindler度规.