利率风险与或有权益定价

应用无差异方法研究不完全市场中或有权益的保值和定价问题,并证明了或有权益的价格不仅依赖于或有权益的不可复制部分,而且受利率风险的影响．在最优保值意义下利率风险分解为可控风险和不可控风险．利率的可控风险与资本市场波动有关,可通过套期保值方法避免,可能产生正、零或负的期望收益．利率的不可控风险与资本市场波动无关,无法对冲,而且带来正的期望收益．利率风险的分解有助于更准确地解释或有权益的价格-它受利率的不可控风险影响,而与可控风险无关．当利率的不可控收益与或有权益的不可复制部分正(负)相关时,或有权益的不可复制部分的风险越大导致或有权益的价格越高(低)．     

强不定问题的变分方法

简要回顾近年来关于强不定问题的变分方法某些研究方面的发展．首先介绍强不定问题,接着叙述建立强不定问题的变分框架的基本思路,进而给出局部凸拓扑线性空间的形变理论,最后陈述几个基于此形变理论的处理强不定问题的临界点定理．这些理论的应用将在后续文章中介绍．     

随机支付型未定权益的风险最小套期保值

讨论了具有随机支付型未定权益的风险最小套期问题.假定市场中存在两类具有不同市场信息的投资者,对于一个预先给定的随机支付流未定权益,利用Galtchouk-Kunita-Watanabe分解和L2空间投影定理证明了风险最小策略的存在性和唯一性,并给出了风险最小策略的构造方法.     

求解标准二次优化问题的割平面算法

标准的二次优化问题是NP-hard问题,把该问题转化为半不定的线性规划问题,且提出了一个线性规划的割平面算法来求解这个半不定的线性规划问题,并给出了该算法的收敛性证明.     

一种非概率的利率模型

对于固定收益产品定价这个问题已经有很多种方法,将从另外一种角度来考虑这个问题,先通过T ay lor展开得到一个双曲型的偏微分方程,利用这个方程可以求出未定权益组合的最好最坏情景下的价格,然后再利用市场上已有的产品对此未定权益静态对冲,将会得到一个收益率曲线包络.     

带交易费的未定权益有偏好套期保值定价

本文首先引进了正常化市场和有偏好套期保值概念，给出了有偏好系数的未定权益套期保值定价．由此进一步给出未定权益的卖方价和买方价，以及未定权益的定价区间．     

考虑死亡风险下权益指数年金的定价

权益指数年金(Equity Indexed Annuities)是欧美市场近十年发展起来的一类新型年金产品,有最小收益保证,在最小保证基础上与预先设定好的某类股指收益相关联．本文在考虑死亡风险情况下,对简单点对点和年度重设两种指数计算方法下权益指数年金的定价问题作了研究,给出了定价公式并对参与率作了敏感性分析．     

一类不定常热耦合Stokes问题:存在性,唯一性和解的爆破

研究了一类具有与时间相关的黏性系数和黏性热的不定常不可压拟牛顿流问题,即一类不定常热耦合Stokes问题.在一定条件下用Schauder不动点定理证明了弱解的存在性.通过建立弱解对初边值的估计式证明了解的唯一性.给出了有关解的爆破的结论.     

基金投资中委托代理问题的博弈分析

由于基金市场中的信息不对称,以及基金管理者和投资者之间的利益不一致,使得逆向选择和道德风险这两类委托代理问题成为基金治理时的核心问题之一,关于它们的研究对于保护投资者权益,发展和完善基金市场都有重要意义.从博弈分析的角度出发,通过建立不同的动态博弈模型,研究了这两类委托代理问题在基金市场上存在的原因以及可能产生的主要影响,并在参数分析的基础上提出了一些解决问题的想法和建议.     

带有交叉项的离散不定随机线性二次控制问题

研究性能指标带有交叉项的离散时间不定随机线性二次(LQ)控制问题，允许权矩阵是不定的。引入一个广义差分Riccati方程，证明了此方程的可解性是LQ问题存在最优控制的一个充分条件，并用方程的解给出了最优控制。推广了[1]的结果。     

Conic coconuts: the pricing of contingent capital notes using conic finance

In this paper we introduce a fundamental model under which we will price contingent capital notes using conic finance techniques. The model is based on more realistic balance-sheet models recognizing the fact that asset and liabilities are both risky and have to be treated differently taking into account bid and ask prices in a prudent fashion. The underlying theory makes use of conic finance which is based on the concept of acceptability and distorted expectations. We recall the theory and give a brief overview of the related literature. Next, we discuss and propose some potential funded and unfunded contingent capital notes. Traditionally, the conversion trigger of contingent capital notes is in terms of the Core-Tier 1 ratio. We argue that this ratio is maybe not optimal, certainly when taking into account the presence of risky liabilities. As an alternative we introduce triggers based on capital shortfall. The pricing of seven variations of funded as well as unfunded notes is overviewed. We further investigate the effect of the dilution factor and the grace factor. In an appendix we show conic balance sheets including contingent capital instruments.     

Lyapunov pairs for multi-valued semi-linear evolutions

We give here a characterization of a Lyapunov pair for a multi-valued semi-linear evolution equation on a Banach space by means of an appropriate lower contingent derivative. The contingent derivative introduced in this paper is related to a new concept of tangency introduced recently in [O. Cârj?, M. Necula, I.I. Vrabie, Necessary and sufficient conditions for viability for semilinear differential inclusions, Trans. Amer. Math. Soc. 361 (2009) 343-390]. As an application, we give a controllability result and a Lipschitz estimate of the corresponding minimum time function under a Petrov-like condition.     

基于遗传算法的附随扩散模型的构建及实证研究

论文研究了具有附随扩散关系的产品扩散特点,以Bass模型为理论基础,构建了附随扩散模型,然后以移动上网用户附随移动用户扩散的实例为研究对象,建立了移动上网附随扩散模型,并采用遗传算法估算模型参数,对今后几年移动上网用户的扩散规律进行了预测。最后,将附随扩散模型的研究结果与采用传统Bass模型、Logistic模聊的结果进行了对比,得出了附随扩散模型拟合和预测效果更好的结论。     

Universal contingent claims in a general market environment and multiplicative measures: Examples and applications

We present and further develop the concept of a universal contingent claim introduced by the author in 1995. This concept provides a unified framework for the analysis of a wide class of financial derivatives.A universal contingent claim describes the time evolution of a contingent payoff. In the simplest case of a European contingent claim, this time evolution is given by a family of nonnegative linear operators, the valuation operators. For more complex contingent claims, the time evolution that is given by the valuation operators can be interrupted by discrete or continuous activation of external influences that are described by, generally speaking, nonlinear operators, the activation operators. For example, Bermudan and American contingent claims represent discretely and continuously activated universal contingent claims with the activation operators being the nonlinear maximum operators.We show that the value of a universal contingent claim is given by a multiplicative measure introduced by the author in 1995. Roughly speaking, a multiplicative measure is an operator-valued (in general, an abstract measure with values in a partial monoid) function on a semiring of sets which is multiplicative on the union of disjoint sets. We also show that the value of a universal contingent claim is determined by a, generally speaking, impulsive semilinear evolution equation.     

Robust mean–variance hedging via G-expectation

In this paper we study mean–variance hedging under the $G$-expectation framework. Our analysis is carried out by exploiting the $G$-martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric $G$-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.     

Optimal control of a dual service rate M/M/1 production-inventory model

We analyse a dual-source, production-inventory model in which the processing times at a primary manufacturing resource and a second, contingent resource are exponentially distributed. We interpret the contingent source to be a subcontractor, although it could also be overtime production. We treat the inventory and contingent sourcing policies as decision variables in an analytical study and, additionally, allow the primary manufacturing capacity to be a decision variable in a subsequent numerical study. Our goal is to gain insight into the use of subcontracting as a contingent source of goods and whether it can fulfill real-world managers' expectations for improved performance. We prove that a stationary, non-randomised inventory and subcontracting policy is optimal for our M/M/1 dual-source model and, moreover, that a dual base-stock policy is optimal. We then derive an exact closed-form expression for one of the optimal base stocks, which to our knowledge is the first closed-form solution for a dual-source model. We use that closed-form result to advantage in a numerical study from which we gain insight into how optimal capacity, subcontracting, and inventory policies are set, and how effectively a contingent source can reduce total cost, capacity cost, and inventory cost. We find that (i) the contingent source can reduce total cost effectively even when contingent sourcing is expensive and (ii) contingent sourcing reduces capacity cost more effectively than it does inventory cost.     

Integrated capacity and inventory management with capacity acquisition lead times

We model a make-to-stock production system that utilizes permanent and contingent capacity to meet non-stationary stochastic demand, where a constant lead time is associated with the acquisition of contingent capacity. We determine the structure of the optimal solution concerning both the operational decisions of integrated inventory and flexible capacity management, and the tactical decision of determining the optimal permanent capacity level. Furthermore, we show that the inventory (either before or after production), the pipeline contingent capacity, the contingent capacity to be ordered, and the permanent capacity are economic substitutes. We also show that the stochastic demand variable and the optimal contingent capacity acquisition decisions are economic complements. Finally, we perform numerical experiments to evaluate the value of utilizing contingent capacity and to study the effects of capacity acquisition lead time, providing useful managerial insights.     

Characterization of Stochastic Viability of Any Nonsmooth Set Involving Its Generalized Contingent Curvature

Abstract

Thanks to the Stroock and Varadhan “Support Theorem” and under convenient regularity assumptions, stochastic viability problems are equivalent to invariance problems for control systems (also called tychastic viability), as it has been singled out by Doss in 1977 for instance. By the way, it is in this framework of invariance under control systems that problems of stochastic viability in mathematical finance are studied. The Invariance Theorem for control systems characterizes invariance through first‐order tangential and/or normal conditions whereas the stochastic invariance theorem characterizes invariance under second‐order tangential conditions. Doss's Theorem states that these first‐order normal conditions are equivalent to second‐order normal conditions that we expect for invariance under stochastic differential equations for smooth subsets. We extend this result to any subset by defining in an adequate way the concept of contingent curvature of a set and contingent epi‐Hessian of a function, related to the contingent curvature of its epigraph. This allows us to go one step further by characterizing functions the epigraphs of which are invariant under systems of stochastic differential equations. We shall show that they are (generalized) solutions to either a system of first‐order Hamilton‐Jacobi equations or to an equivalent system of second‐order Hamilton‐Jacobi equations.     

突发事件冲击下基于或有支付机制的创投融资决策

探讨了突发事件冲击下基于或有支付机制的创业融资优化决策问题.假定创业企业利润流服从跳跃-扩散过程,运用实物期权方法推导出投资机会价值与最优投资时机,给出了最优的或有支付决策,使得创业企业家和风险投资家愿意共同支持给定的创业企业的增长策略.研究发现,突发事件时创业企业家和风险投资家的最优投资时机不受或有支付类型的影响.突发事件的平均发生率越大,双方共同投资的时机越早.利润流跳跃幅度越大,共同投资的时机也越早.目标实现时刻进行支付的或有支付具有更高的投资机会价值,可变数额或有支付具有更高的投资机会价值.