高科技公司的合理定价

在随机控制的框架下，给出了一般的合理定价高科技公司的模型，考虑到高科技公司的管理柔性，采用动态规划和实物期权定价思想和方法，给出高科技公司价值所满足的偏微分方程，在特殊情况下，给出解析解，讨论了参数的影响，最后，给出一个应用实例。     

用实物期权分析方法评价高科技公司

在实物期权分析理论的框架下,开发了更一般的评价高科技公司的模型.利用随机动态规划和实物期权理论,本文得到了高科技公司价值所满足的偏微分方程.在特殊情况下,给出了解析解,并分析参数对高科技价值的影响,最后,给出一个实例来说明本文的结论.     

有交易费时的欧式期权定价

本文考虑存款与借款利率不同且对股票的交易有交易费要求时的欧式期权定价问题。我们假定投资者的投资目的是使自己的期望效用最大化。对于市场给出的期权价格,投资者将选择最优的资产组合。在投资者的这种行为下,可以认为市场是投资者的对手,而期权的市场价格将会这样给出：投资者在这个价格下,他的最大期望效用将达到最小。本文在假定投资者的效用函数为风险中性时,给出了有交易费时欧式期权价格的显式表达式。     

期权视角下房屋预售合约定价模型

房屋预售合约赋予了购房者以给定的价格购买房屋的权利,具有期权性质。首先基于房地产市场具有摩擦的事实,将房屋预售合约视为房价的期权合约,然后通过将房价演变过程模型化为Ornstein-Uhlenbeck过程,导出了预售合约的合理价格(即首付)的解析表达式,最后比较了采用几何布朗运动与Ornstein-Uhlenbeck过程模拟房价变化所得房屋预售价格的差异。结论认为,基于Ornstein-Uhlenbeck过程导出的房屋预售合约价格相较于几何布朗运动下的预售合约价格具有更小的套利空间。     

POLLUTION, GOVERNMENT EXPENDITURE, TAXES AND STOCHASTIC GROWTH

This paper studies a stochastic endogenous growth model with pollution. It introduces government expenditure and exogenous pollution abatement technology to eliminate pollution and proves that under appropriate equilibrium conditions the main economic indexes （including economic growth rate, the optimal government expenditure rate） in the centrally planned economy and decentralized economy can be expressed by the parameters of the model uniquely. The optimal tax policy is analyzed ,and the optimal pollution is derived.     

需求随机下房地产开发商最优进入-退出与能力扩张决策模型

在租赁市场上,房地产开发商常常需要同时决定进入-退出时机及开发能力扩张的的时机.然而这一研究在已往的房地产投资有关文献中有所忽视.鉴于此,在需求随机的条件下,通过一两阶段决策模型同时研究了房地产开发商在租赁市场的进入-退出及能力扩张问题.指出了进入、退出决策的隐式解并给出了扩张决策的阀值及扩张投资额度.研究同时得出结论:不确定性与成本的提高会增大了开发商进入-退出的决策刚性,并同时抑制了开发商的扩张投资.文章同时在行文中分析了结论的经济含义与政策含义.     

风险投资的多阶段复合实物期权定价方法

根据风险投资的多阶段连续性,建立多阶段复合实物期权定价模型,并利用条件期望和矩阵性质推导出该期权的定价公式,定价方法可用于风险投资项目的评估和决策.     

两股票情形下欧式期权定价新方法

假定股票价格服从布朗运动驱动的随机微分方程,从随机动力学的角度出发考虑欧式期权定价问题.由Fokker-Planck-Kolmogrov得到了股票价格过程的概率转移密度函数,基于此,可以求得两股票情形下各种欧式类型未定权益的定价公式.为欧式期权定价提供了一个新方法.     

基于模糊Black-Scholes模型的螺纹钢期权定价

能源金融和大宗商品的衍生品交易已逐渐成为金融领域的前沿热点问题。钢铁类金融衍生品定价和能源金融风险研究,对能源资产证券化和金融的发展有着重要意义。本文在现有的期权定价模型下,结合影响螺纹钢实物期权价格的因素,优化经典的Black-Scholes实物期权定价模型,得到螺纹钢模糊B-S实物期权定价模型,并结合VaR方法,研究螺纹钢实物期权的定价机制,量化钢铁类金融风险,从而合理的控制风险传播。     

具有生产性与福利性公共支出的随机内生增长模型

文章建立一个随机内生增长模型来阐明主要政策参数对经济增长与社会福利的影响.若对生产函数、效用函数、偏好及随机干扰作一些特殊的假设,我们证明了主要政策参数的均衡值能被模型参数唯一决定.进一步我们还得到了期望增长率与储蓄的清晰解.文章的最后,我们证明了政府支出直接影响个体决策者的决策:即提高经济增长率将减少福利;反之,增加福利将减少增长率.     

在未来收益不确定下的期权定价模型

§ 1　 IntroductionAt present,some high-technology(high-tech) firms such as information,software,pharmaceutical et al,are rapidly growing at home and abroad.The firm' s stock price hasbeen bid upward irrationally by individual day traders.Some managers see the currentfren-zy as a spectacularexample ofmarketbubble.The marketbubble can' tbe explained by theaverage rate of growth,butithas reacted on the developmentprospect of high-tech firms.Existing net cash flow method cannot properly capture …     

Optimal Trade Execution Under Stochastic Volatility and Liquidity

Abstract

We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential or a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases, we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases, we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo (1998; Optimal control of execution costs. Journal of Financial Markets, 1, 1–50) and Almgren and Chriss (2001; Optimal execution of portfolio transactions. Journal of Risk, 3, 5–33).     

HETEROGENEOUS INFORMATION ARRIVAL AND R＆D OPTION PRICING

The paper models the arrival of heterogeneous information during R&D stages as a doubly stochastic Poisson process(DSPP). The new product market introduction is considered as a timing option(an American perpetual option). Investment in R&D can be thought of as option on an option(a compound option). This paper derives an analytic approximation valuation formula for the R&D option, and demonstrates that the accounts for heterogeneous information arrival may reduce the pricing biases. This way, the gap between real option theory and the practice of decision making with respect to investment in R&D is diminished.     

Existence of an optimal control for a coupled FBSDE with a non degenerate diffusion coefficient

We consider a controlled system driven by a coupled forward–backward stochastic differential equation with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential equation, at the initial time. Our goal is to find an optimal control which minimizes the cost functional. The method consists to construct a sequence of approximating controlled systems for which we show the existence of a sequence of feedback optimal controls. By passing to the limit, we establish the existence of a relaxed optimal control to the initial problem. The existence of a strict control follows from the Filippov convexity condition.     

Controlled diffusions in a random medium

Using homogenization theory we treat the problem of controlled diffusions in a random medium with rapidly varying composition. This involves homogenization of a nonlinear Bellman dynamic programming equation wtih rapidly varying random coefficients. The appropriate "averaged form" of this equation is derived to define the limiting contrl problem; and a precise convergence result is given     

Stochastic Optimal Control for the Stochastic Heat Equation with Exponentially Growing Coefficients and with Control and Noise on a Subdomain

Abstract

We consider stochastic optimal control problems in Banach spaces, related to nonlinear controlled equations with dissipative non linearities: on the nonlinear term we do not impose any growth condition. The problems are treated via the backward stochastic differential equations approach, that allows also to solve in mild sense Hamilton Jacobi Bellman equations in Banach spaces. We apply the results to controlled stochastic heat equation, in space dimension 1, with control and noise acting on a subdomain.     

Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton–Jacobi–Bellman equation. These results are applied to some controlled stochastic partial differential equations.