Optimal consumption and investment problem with random horizon in a BMAP model

In this paper, we consider the consumption and investment problem with random horizon in a Batch Markov Arrival Process (BMAP) model. The investor invests her wealth in a financial market consisting of a risk-free asset and a risky asset. The price processes of the riskless asset and the risky asset are modulated by a continuous-time Markov chain, which is the phase process of a BMAP. The possible consumption or investment are restricted to a sequence of random discrete time points which are determined by the same BMAP. The investor has only consumption opportunities at some of these random time points, has both consumption and investment opportunities at some other random time points, and can do nothing at the remaining random time points. The object of the investor is to select the consumption–investment strategy that maximizes the expected total discounted utility. The purpose of this paper is to analyze the impact of the consumption–investment opportunity and the economic state on the value functions and consumption–investment strategies. The general solution and the exact solution under the assumption that the consumption and the terminal wealth are evaluated by the power utility are obtained. Finally, a numerical example is presented.     

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function ofbosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced ingeneralized uncertainty principle takes a proper value, we derive Bekenstein-Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small massapproximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropyof the black string cosmological horizon in non-spherical coordinate spacetime.     

Necessary conditions for infinite-horizon Volterra optimal control problems with time delay

Email: csfvega{at}dm.uba.ar Received on August 17, 2006; Accepted on September 8, 2007 Necessary conditions are proved for optimal control problemsinvolving an infinite horizon and terminal conditions at infinitywhose states are governed by Volterra integral equations withnon-linear time delay.     

动态广义球对称含荷黑洞对Dirac粒子的热辐射

分析讨论动态广义球对称含荷黑洞视界附近的狄拉克方程,准确地定出了动态广义球对称含荷黑洞的Hawking温度和辐射谱,同时计算出事件视界方程,所得结果与用零曲面方程得到的结果一致。     

Asymptotic properties of constrained Markov Decision Processes

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of finite horizon MDPs to the infinite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with infinite state space, (3) convergence of MDPs as the discount factor goes to a limit. In all these cases we establish the convergence of optimal values and policies. Moreover, based on the optimal policy for the limiting problem, we construct policies which are almost optimal for the other (approximating) problems. Based on the convergence of MDPs with a truncated state space to the problem with infinite state space, we show that an optimal stationary policy exists such that the number of randomisations it uses is less or equal to the number of constraints plus one. We finally apply the results to a dynamic scheduling problem.This work was partially supported by the Chateaubriand fellowship from the French embassy in Israel and by the European Grant BRA-QMIPS of CEC DG XIII     

内蒙古黄岗梁-白音诺土壤地球化学方法探讨

根据内蒙古黄岗梁—白音诺半干旱区的特点，从研究风成沙对本区土壤地球化学影响入手，进行了土壤的层位及粒度的研究，以确定该区在野外实际工作中土壤地球化学勘查方法所采取的粒级区间和层位。结果表明，土壤测量应截取-5mm～ 0.45mm粒级，层位为c层样品，可有效排除风沙的干扰。     

两淮煤田石炭二叠煤系气源岩评价及其煤成气资源量估算

在有机岩石学参数和有机地球化学参数大量数据的基础上,研究了有机质丰度、有机质类型及有机质成熟度的成烃三要素,确认本区这套源层的有机质丰度高,有机质类型属腐植型(Ⅲ型)母质,有不同程度上的偏混合型(Ⅱ型)特征:有机质成熟度属成熟(淮南)到过成熟(淮北大部)阶段。深成变质作用和后期岩浆热变质作用的迭加是造成两淮煤田现今煤级分布格局的基本因素,雄厚的物质基础、良好的母质类型和适宜的成熟程度表明,本区石炭三叠煤系有良好的产气前景     

Degeneracy in infinite horizon optimization

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.This material is based on work supported by the National Science Foundation under Grants ECS-8409682 and ECS-8700836.