具有一般跳幅度分布的跳扩散模型下永久公司债券的定价

在公司资产价值演化服从具有一般跳幅度分布的跳扩散模型下,采用结构化方法研究具有无限到期日公司债券的定价问题,通过微分方程的方法和无套利原理获得了公司债券,股东权益和公司总价值的定价表达式以及最佳违约边界的表达式.     

具有跳扩散模型下永久公司债券的定价和最佳资产结构

综合运用偏微分方程方法和结构化方法,在公司资产价值演化服从跳扩散模型下,研究永久公司债券的定价问题和最佳资产结构问题,获得了公司债券,股东权益和公司总价值的定价表达式和最佳杠杆比率的表达式.     

试论非完全信息下债权人和股东的博弈均衡

本文研究当公司信息披露时间不确定、而信息披露时投资者可以完全了解公司的真实价值的情况下,投资者和股东的决策问题。运用博弈的思想,得到均衡条件下投资者对公司债务安全条款的阈值的最优选择及股东对信息披露的最优控制。结果显示理性的股东应该选择完全的信息披露。     

The pricing of perpetual convertible bond with credit risk

Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.     

政府投资环保的随机增长模型

本文分析了一个带有污染的随机内生增长模型.利用随机最优化的方法,求出了最优的政府环保投资比率和最优的税收政策.并进一步得出了最优的收入税因污染的外部性指标、生产的扰动的增大而减少;而最优消费税则因这两个参数的增大而增加的结论.     

Perpetual convertible bonds with credit risk

A convertible bond is a security that the holder can convert into a specified number of underlying shares. We enrich the standard model by introducing some default risk of the issuer. Once default has occured payments stop immediately. In the context of a reduced form model with infinite time horizon driven by a Brownian motion, analytical formulae for the no-arbitrage price of this American contingent claim are obtained and characterised in terms of solutions of free boundary problems. It turns out that the default risk changes the structure of the optimal stopping strategy essentially. Especially, the continuation region may become a disconnected subset of the state space.     

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This paper establish a first passage time model basedon the Merton's structural model by using the method of geometric Brownianmotion. In this paper, we consider the accounting noise and historical defaultrecord and then introduce a new incomplete information hypothesis. Besides,we introduce the stock's liquidity value into the model, and apply its methodmeasurement which based on Merton's structural model to the first passagetime model to obtain the endogenous default boundary. Based on the incompleteinformation, the conditional default probability is derived by using thedefault boundary. And at the last of this passage, we analysis the effectof the correlation between stock's price and company assets on the defaultprobability.     

Existence and explicit determination of optimal stopping times

We consider large classes of continuous time optimal stopping problems for which we establish the existence and form of the optimal stopping times. These optimal times are then used to find approximate optimal solutions for a class of discrete time problems.     

Optimal stopping for extremal processes

For an extremal process (Z_t)_t the optimal stopping problem for X_t = f(Z_t)?g(t) gives the continuous time analogue of the optimal stopping problem for max{Y₁,…,Y_k}?c_k where Y₁, Y₂,… are i.i.d. For the continuous time problem we derive optimal stopping times in explicit form and also show that the optimal stopping boundary is the limit of the optimal stopping boundaries for suitably standardized discrete problems.     

Bivariate lifetime distributions and optimal replacement

The assumption that components which are part of a technical system work independently seems not appropriate in a number of applications. A lot of multivariate extensions of the univariate exponential distribution have been suggested as lifetime distributions. But only the models of J. E. Freund and of A. W. Marshall and I. Olkin seem to be physically motivated. A combination of these approaches yields a bivariate lifetime distribution which is investigated in some detail. Applications of this bivariate lifetime model are considered in preventive maintenance. In a two-component parallel system the optimal replacement time shall be determined with respect to the total expected discounted cost criterion. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Some numerical examples based on a two-component parallel system with dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components.     

A general replacement model

Summary Replacement models deal with the problem of finding the optimal random time for a preventive replacement of a technical system. A large class of such models has been considered in the literature recently. In this paper a unifying approach to the replacement problem is given regarding it as an optimal stopping problem. The generalization allows to weaken a necessary monotonicity condition and to consider different information levels. Measuring information in this context leads to discussing the problem in general terms of stochastic process theory. An example shows how to get explicit solutions and how the information level influences the optimal replacement policy.

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Zusammenfassung Ersetzungsmodelle beschreiben im Rahmen der Zuverlässigkeitstheorie das Problem, einen optimalen Zeitpunkt für die vorbeugende Ersetzung eines technischen Systems festzulegen. Eine große Vielfalt solcher Modelle ist in letzter Zeit in der Literatur zu finden. Ziel dieser Arbeit ist es, einen einheitlichen Zugang zu dem Ersetzungsproblem anzugeben, indem dieses Problem als Problem des optimalen Stoppens aufgefaßt wird. Die Verallgemeinerung vorhandener Modelle erlaubt es, eine notwendige Monotoniebedingung abzuschwächen und unterschiedliche Informationsniveaus zu betrachten. An einem Beispiel wird gezeigt, wie sich explizite Lösungen des Ersetzungsproblems gewinnen lassen und wie sich das Informationsniveau auf die optimale Ersetzungsstrategie auswirkt.

     

信用违约互换的定价方法

通过对信用违约互换的结构的分析,在Merton的结构化方法框架下,用偏微分方程求出公司的违约概率密度,最后给出信用违约互换的一种定价方法.     

The best choice problem with an unknown number of objects

The secretary problem with a known prior distribution of the number of candidates is considered. Ifp(i)=p(N=i),i [, ] , where=inf{i :p(i) > 0} and=sup{i :p(i)0}, is the prior distribution of the numberN of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping indexj=min satisfies asymptotically (as ) the equationj=exp .The probability of selecting the best object by the corresponding policy will be (j-1) p(i)/i. We also give an example of the distributionp for which the optimal stopping rule consists of a stopping set with two islands. We present an asymptotical solution for this example.     

股票操作选时的最优停止问题

股票操作中的选时即决定何时买进何时卖出是人们进行操作时最为关心的,本文运用最优停止及时间序更的理论和方法,给出了一种较优的具体操作方法。     

Prophet inequalities for parallel processes

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then

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and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.