高校应用数学学报第二十卷A辑（中文版）总目次

第1期2005年3月一类证券市场中投资组合及消费选择的最优控制问题史敬涛吴臻(1)…………………………………………………股票收益率波动性的非参数核回归估计及对中国股市的实证分析鲁万波李竹渝(9)……………………………………带交易费的终端资产和消费的期望贴现效用最大化赵小艳聂赞坎(17)…………………………………………………r=q时美式期权最佳实施边界在到期日附近的渐近展开万凝(24)………………………………………………………更新风险模型中破产概率的一个局部结果毕秀春尹传存(29)…………………………………………………………     

Vasicek利率模型下带有零息票债券的投资-消费模型

应用随机最优控制理论研究Vasicek利率模型下的投资-消费问题,其中假设无风险利率是服从Vasicek利率模型的随机过程,且与股票价格过程存在一般相关性.假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成,投资者的目标是最大化中期消费与终端财富的期望贴现效用.应用变量替换方法得到了幂效用下最优投资-消费策略的显示表达式,并分析了最优投资-消费策略对市场参数的灵敏度.     

一类连续最优控制问题的有限维近似

1　引　　言本文考虑具有状态终端约束、控制受限的非线性连续最优控制问题min　h0(x(0))+∫T0f0(x(t),u(t))dt+g0(x(T))(1.1)s.t.　x(t)=f(x(t),u(t)),　　t∈[0,T](1.2)D(x(0))=0,(1.3)E(x(T))=0,(1.4)S(u(t))≤0,　　t∈[0,T](1.5)其中,h0:Rn→R,f0:Rn×Rm→R,f:Rn×Rm→Rn,g0:Rn→R,D:Rn→Rp,E:Rn→Rq,S:Rm→Rr均为二次连续可微函数.T为终端时间(固定),p,q≤n,x(t)∈W1,∞[0,T]n,u(t)∈L∞[0,T]m分别为状态函数和控制函数.U(t)={u:S(u(t))≤0}为紧凸集.问题(1.1)—(1.5)要求寻找最佳控制u(t)使得目标函数(1.1)达到极小.…     

碳约束下的中国省际电能终端消费——效率测度及影响因素研究

提出包含非期望产出的博弈交叉-Malmquist全要素生产率指数模型,利用该模型对中国2002-2014年30个省份的电力能源面板数据进行电力能源终端消费效率评价,并采用SYS-GMM动态面板模型对其影响因素进行分析。研究发现:(1)我国省际电力能源终端利用效率出现负增长,技术效率变动和技术变动是引发该问题两大因素。(2)我国经济相对落后的西北地区借助技术效率的后发优势,在电能终端消费效率的排序中跻身榜首,其次是华北和东北地区,而华东、华中和南方地区则处于末位。(3)电力能源效率具有传递效应,其前期表现会对现期产生显著影响,此外电力价格、对外开放程度和技术进步对电力能源效率具有正向影响,而产业结构与电力能源效率具有负相关关系。     

个人投资与消费模型的期望效用最大化

研究了具有初始财富的投资者如何最大化终端资产和消费的期望效用,首先通过交易费用函数建立带交易费的连续时间投资与消费模型,然后运用鞅分析和对偶理论证明了：在有效市场中,如果投资者积极交易,则只会降低终端财富的期望值,并得到了最优投资消费组合过程和终端资产.     

触销式双障碍卖权价值过程分析及其定价

主要证明了在不存在交易成本的完全市场条件下连续时间欧式触销式双障碍卖权贴现到0时刻的价值过程{V(t∧τL∧τH,Sl∧τL∧τH)；0≤t≤T}为鞅，并且给出了对应单障碍卖权价值过程的鞅性质。同时还讨论了美式触销式双障碍卖权的定价问题，给出了任意时刻t(0≤t≤T)其内在价值的表达式。     

Markov过程最优控制的最大值原理

本文在终端时间T固定,目标集是L~2(Ω,?T,P;R~n)中的具有限余维数的相对凸体的情况下,对一般指标Markov过程最优控制问题证明了最大值原理。本文主要采用向量测度值域定理的方法。     

重复采购竞拍中两种卡特尔串谋机制稳定性的边界条件研究

深入研究临界贴现因子和保留价格两种因素对重复采购竞拍中的两种卡特尔串谋机制稳定性的影响。研究表明:(1)当串谋成员的贴现因子超过临界贴现因子时,没有成员会背叛串谋协定;(2)相比简单保留价格和纳什均衡保留价格,本文提出的阻挠串谋的最小保留价格最能有效阻止销售方串谋行为并确保采购方一定收益。研究结果有助于增进对重复采购拍卖下两种卡特尔串谋机制的运作机理的理解,丰富了重复采购环境下竞拍串谋监管机制和策略的理论研究内容。     

有资助的消费和最终资产的效用最大化

本文主要讨论带有随机资助过程的消费和终端财富效用最大化问题 .当对偶域为 (L∞) 时 ,利用对偶方法 ,求得问题的最优解对().     

有限期限上具有随机利率的最优投资消费模型

文章考虑有限期限上的最优投资消费问题.风险资产服从几何布朗运动,利率服从一个遍历的Markov过程.目标是累积消费和终值财富贴现的幂效用期望最大化.利用动态规划原理推导出值函数所满足的HJB方程,并利用上下解方法证明了对应非线性抛物型偏微分方程终值问题解的存在唯一性,最后证明了验证性定理.     

Optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints

In this paper, we consider the optimal consumption and portfolio policies with the consumption habit constraints and the terminal wealth downside constraints, that is, here the consumption rate is greater than or equal to some nonnegative process, and the terminal wealth is no less than some positive constant. Using the martingale approach, we get the optimal consumption and portfolio policies.     

Optimal investment and consumption models with non-linear stock dynamics

We study a generalization of the Merton's original problem of optimal consumption and portfolio choice for a single investor in an intertemporal economy. The agent trades between a bond and a stock account and he may consume out of his bond holdings. The price of the bond is deterministic as opposed to the stock price which is modelled as a diffusion process. The main assumption is that the coefficients of the stock price diffusion are arbitrary nonlinear functions of the underlying process. The investor's goal is to maximize his expected utility from terminal wealth and/or his expected utility of intermediate consumption. The individual preferences are of Constant Relative Risk Aversion (CRRA) type for both the consumption stream and the terminal wealth. Employing a novel transformation, we are able to produce closed form solutions for the value function and the optimal policies. In the absence of intermediate consumption, the value function can be expressed in terms of a power of the solution of a homogeneous linear parabolic equation. When intermediate consumption is allowed, the value function is expressed via the solution of a non-homogeneous linear parabolic equation.     

A dynamic programming approach to constrained portfolios

This paper studies constrained portfolio problems that may involve constraints on the probability or the expected size of a shortfall of wealth or consumption. Our first contribution is that we solve the problems by dynamic programming, which is in contrast to the existing literature that applies the martingale method. More precisely, we construct the non-separable value function by formalizing the optimal constrained terminal wealth to be a (conjectured) contingent claim on the optimal non-constrained terminal wealth. This is relevant by itself, but also opens up the opportunity to derive new solutions to constrained problems. As a second contribution, we thus derive new results for non-strict constraints on the shortfall of intermediate wealth and/or consumption.     

Risk averse asymptotics in a Black–Scholes market on a finite time horizon

We consider the optimal investment and consumption problem in a Black–Scholes market, if the target functional is given by expected discounted utility of consumption plus expected discounted utility of terminal wealth. We investigate the behaviour of the optimal strategies, if the relative risk aversion tends to infinity. It turns out that the limiting strategies are: do not invest at all in the stock market and keep the rate of consumption constant!     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

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.     

The path player game

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption undermodel uncertainty. The underlying market model consists of a risky asset, whosevolatility and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with risk aversionparameter 0 < α < 1 and a dynamically consistent coherent risk measure, whichallows for model uncertainty in the distributions of both the asset price dynamics andthe factor process. Ourmethod combines recent results by Wittmüß (Robust optimizationof consumption with random endowment, 2006) on the duality theory of robustoptimization of consumption with a stochastic control approach to the dual problemof determining a ‘worst-case martingale measure’.     

Dual method for continuous-time Markowitz's problems with nonlinear wealth equations

Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal wealth and portfolio is the solution of a forward-backward stochastic differential equation with constraints.