积分第一中值定理的逆问题及其推广

本本文给出了推广的积分第一中值定理的概念及定义,并在此基础上对第一中值定理的逆问题加以证明,进而对二维积分中值定理逆问题证明。     

积分第一中值定理的逆问题及其推广

本本文给出了推广的积分第一中值定理的概念及定义,并在此基础上对第一中值定理的逆问题加以证明,进而对二维积分中值定理逆问题证明.     

指数导数的微分中值定理

本文证明了反函数的指数导数求导法则.在指数导数意义下建立了著名的罗尔定理,拉格朗日中值定理和柯西中值定理。     

罗尔中值定理的推广

本文将微积分中的罗尔定理从有限闭区间推广到了半无限区间和无限区间,有助于对罗尔中值定理的理解.     

Lagrange中值定理的几种证明方法及其推广

拉格朗日(Lagrange)微分中值定理在数学分析中占有重要地位,然而多年来其证明方法单一,为弥补此不足,本文列出了证明该定理的几种不同的方法及一个推广,以使读者更深刻的理解。     

Black-Scholes微分方程假设条件分析

本文首先证明了Black-Scholes微分方程只是含贴现的费曼-卡茨定理的一个特殊形式,含贴现的费曼-卡茨定理是Black-Scholes微分方程的必要条件。然后从含贴现的费曼-卡茨定理出发来研究Black-Scholes微分方程的基本假设条件。     

浅谈科斯第二定理的质疑

科斯第一定理概括为当交易成本为零时,无论产权在法律上如何安排,私人谈判都会导致资源的优化配置。但是在现实生活中由于信息的不对称,交易成本不可能无为零,当交易成本很高,足以阻止谈判时,有效的资源利用将取决于产权的安排,这就是所谓的科斯第二定理,虽然这些理论极大的推动法和法和经济的拓展,但是本身也存严重的缺陷。     

拉格朗日中值定理的一个证明

拉格朗日中值定理作为高等数学的一个重要定理，在传统的教材中已有证明，本给出此定理的又一证法。     

回到“定分”经济学： 法律经济学对科斯定理的误读与澄清

科斯定理面世至今,不管是在经济学界还是法学界,均存在对该定理的诸多理论误读。从科斯一以贯之的理论逻辑出发,基于一般化的交易成本概念和比较制度分析进路,科斯定理的重点是科斯第二定理（或科斯定律）,即一种“经济的法律分析”。但基于新古典经济学的最优化思维,波斯纳错将科斯第一定理视作科斯定理的核心和重点,不仅将该定理内在的财富最大化视为法律（包括立法和司法）的应然目标,也将最优化模型视为法学研究的基本方法。这是一种将法律视为新古典经济学最优理论之新殖民地的“法律的经济分析”。该理论不仅与科斯经济学背道而驰,还导致了国内法学界在科斯定理上的误判和误用。基于此,我们应该回归科斯所提倡的一种基于比较制度分析的定分经济学。     

浅谈科斯第一定理的质疑

科斯《企业性质》和《社会成本问题》的发表,交易成本概念首次被提出,掀起了新经济制度的浪潮,开辟了崭新的研究领域。科斯第一定理概括为当交易成本为零时,无论产权在法律上如何安排,私人谈判都会导致资源的优化配置,但是这个理论的也存在其不确定行,和不可靠性,文章就对此理论质疑方面进行分析。     

Hazard rate for credit risk and hedging defaultable contingent claims

We provide a concise exposition of theoretical results that appear in modeling default time as a random time, we study in details the invariance martingale property and we establish a representation theorem which leads, in a complete market setting, to the hedging portfolio of a vulnerable claim. Our main result is that, to hedge a defaultable claim one has to invest the value of this contingent claim in the defaultable zero-coupon.Received: April 2003Mathematics Subject Classification: 91B24, 91B29, 60G46JEL Classification: G10The authors would like to thank D. Becherer and J.N. Hugonnier for interesting discussions and the anonymous referee whose pertinent questions on the first version of this paper help them to clarify the proofs. All remaining errors are ours.     

公司价值理论与股票定价

经济金融化使现代公司财务理论从以往的边缘地位逐步朝着金融经济学的核心与主流方向发展。公司价值理论作为现代公司财务伯重要组成部分已日臻完善和成熟。我国长期对公司价值理论研究的忽视，不仅是企业落后的深层原因，而且也是影响市场发展重要因素之一，因为股票价值与公司价值直接相关，忽视公司价值而形成的股票价格不仅是不合理的，而且会对股票市场产生不良影响。     

Negative Libor rates in the swap market model

We apply Stroock and Varadhan’s support theorem to show that there is a positive probability that within the Swap Market Model the implied Libor rates become negative in finite time. Mataix-Pastor received support from the Instituto Credito Oficial (ICO), Spain, and Fundación Caja Madrid.     

Modelling mean reversion of asset prices towards their fundamental value

In this paper we extend the study of mean reversion behavior by modelling the fundamental value as a stochastic process. The market value of the asset is then modelled as a mean reverting Ornstein Uhlenbeck process towards the fundamental value. Solving backwards, we determine the functional form of the regression equation of changes in asset prices and returns to changes to the fundamental value. Using earnings and dividends as proxies for the fundamental value we test our model empirically. In general, other than the shortest horizon of 1-year, our model shows good explanatory power. Since our model is compatible with Campbell and Shiller (1988) framework in the earnings case and Fama and French (1988) model in the dividend case, the performance of our model has been compared with those two models. In comparison, the performance of our model is comparable to that of Campbell and Shiller and compares favorably with Fama and French.     

Diffidence Theorem, State-Dependent Preferences, and DARA

C. Gollier (The Economics of Risk and Time. Cambridge: MIT Press, 2001) has developed a standard technique based on the diffidence theorem. This theorem provides a very simple instrument to solve relatively sophisticated problems when preferences are state-independent. The object of this article is to show that the theorem is also very useful to derive significant results with state-dependent preferences. Using the reference set notion and an extension of the diffidence theorem, we establish formally necessary and sufficient conditions on the reference set, in order to obtain prudence and decreasing absolute risk aversion. Examples of DARA utility functions compatible with non-linear reference sets are presented in the Appendix.     

No Arbitrage Condition for Positive Diffusion Price Processes

Using the Ray-Knight theorem we give conditions for anonnegative diffusion without drift to reach zero or not. These results also givenecessary and sufficient conditions for such a diffusion process to be a martingale (and notjust a local martinagle). We apply these results in order to give necessary and sufficientconditions for nonnegative diffusion to have equivalent local martingale measures.     

Human Capital and Stock Returns: Is the Value Premium an Approximation for Return on Human Capital?

This study, using a direct measure of the wage growth rate within firms, examines the value premium in relation to human capital. The results suggest that the dispersion in wage growth in value and growth stocks explains a large portion of the differences in stock returns. It appears that value stocks are less exposed to shocks in rents to human capital. Differences in labor force characteristics among value and growth stocks also proved to be an important factor in determining both the impact of future changes in labor income growth rate and firm value. The present findings are understood to mean that the ability of investors to forecast the dispersion in wage growth in firms is limited.     

An Aggregation Theorem for the Valuation of Equity Under Linear Information Dynamics

We state an Aggregation Theorem which shows that the recursion value of equity is functionally proportional to its adaptation value. Since the recursion value of equity is equal to its book value plus the expected present value of its abnormal earnings, it follows that the adaptation value of equity can normally be determined by a process of simple quadrature. We demonstrate the application of the Aggregation Theorem using two stochastic processes. The first uses the linear information dynamics of the Ohlson (1995) model. The second uses linear information dynamics based on the Cox, Ingersoll and Ross (1985)'square root' process. Both these processes lead to closed form expressions for the adaptation and overall market value of equity. There are, however, many other processes which are compatible with the Aggregation Theorem. These all show that the market value of equity will be a highly convex function of its recursion value. The empirical evidence we report for UK companies largely supports the convexity hypothesis.     

On relief value (deprival value) versus fair value measurement for contract liabilities: a comment and a response

Horton, Macve and Serafeim (2011) (HMS) argue for the use of relief value for the measurement of certain types of liabilities, and that the replacement liability (an entry price) is normally the appropriate measure of relief. I had previously argued elsewhere for an exit price (normally, the performance value, PV). In this paper, I first try to clarify the terminology used, and then I show why PV rather than RL is usually appropriate for the industries in HMS' example and for some others. My scope is more modest than that of HMS because I do not address revenue/profit issues, which I think should be dealt with separately.