综合孔径辐射成像系统的轨道摄动误差修正

为了提高综合孔径辐射成像系统在地球物理摄动因素影响下的图像精度，对低轨星载综合孔径辐射成像系统的成像误差的修正方法进行了研究，提出了针对地球形状摄动、大气阻力摄动以及两种摄动共同作用的空域补偿动力学模型，结合空域摄动法和数值分析方法对这一空域误差补偿动力学模型进行了模型简化以及误差补偿算法的研究，并给出了空域补偿算法的流程图。仿真结果表明，所提出的空域补偿算法极大地提高了综合孔径辐射成像系统对于目标场景物体的恢复精度，有效降低了综合孔径辐射成像系统成像的摄动力误差。     

航班扰动情形下的飞机路线恢复研究

针对机场临时关闭或飞机停场等造成航班计划扰动的情形,为减少航空公司恢复成本,同时考虑延迟航班、取消航班、替换飞机及摆渡飞机4种策略对飞机路线进行恢复与调整.对经典离散时空网络进行改进,增加摆渡边和替换边,建立以航空公司恢复飞机路线成本最小为目标函数的数学模型,采用CPLEX优化软件求解,对比不同恢复方案的结果.实验结果表明,在航班扰动情形下,同时采取4种恢复策略的方案最优,模型可在有限时间内为航空公司提供较优的恢复方案,具有一定可行性.     

A UNIFIED FRAMEWORK FOR PRICING CREDIT AND EQUITY DERIVATIVES

We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid, or over‐the‐counter derivatives. We observe that our model matches the equity option implied volatility surface well since we properly account for the default risk in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque et al., which only accounts for stochastic volatility.     

PRICING AND HEDGING AMERICAN OPTIONS ANALYTICALLY: A PERTURBATION METHOD

This paper studies the critical stock price of American options with continuous dividend yield. We solve the integral equation and derive a new analytical formula in a series form for the critical stock price. American options can be priced and hedged analytically with the help of our critical-stock-price formula. Numerical tests show that our formula gives very accurate prices. With the error well controlled, our formula is now ready for traders to use in pricing and hedging the S&P 100 index options and for the Chicago Board Options Exchange to use in computing the VXO volatility index.     

奇异摄动问题的LDG／FEM耦合解法

根据奇异摄动问题解的特点，提出了一种求解奇异摄动问题的新方法——LDG／FEM耦合方法．该方法将计算区域分为两个不重叠的子区域，在解变化较大的区域采用具有较好稳定性的间断有限元方法，在解变化平缓的区域采用自由度较少的连续有限元方法．证明了该耦舍方法导出的离散系统的解的存在性和唯一性，并证明了该方法的稳定性．数值结果表明：LDG／FEM耦合方法在Shishkin网格上是一致收敛的．     

绝对有源二端口网络S参数存在范围的研究

本文将给出绝对有源二端口网络S参数的存在范围。这个存在范围的边界是针对|S_(22)|,|S_(11)|平面内,散射矩阵元S_(11)和S_(22)的模的大小给出的。研究表明:在已给出S参数四个模中的三个和四个幅角的情况下,绝对有源条件通常给出散射参数的第四个模的上、下限。在文章的最后将给出一些简单的例子,以说明理论结果的有效性。     

DOES NEAR‐RATIONALITY MATTER IN FIRST‐ORDER APPROXIMATE SOLUTIONS? A PERTURBATION APPROACH

This paper studies first‐order approximate solutions to near‐rational dynamic equilibrium models. Under near‐rationality, agents' subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. In most applications, the beliefs distortion process is also directly observed by (a subset of) the decision‐makers – e.g., ambiguity‐averse households or policy‐makers with a concern for robustness – and therefore included into their optimization problems. We investigate conditions for existence and local uniqueness of solutions under endogenous distortions, as well as the relation with their rational expectations counterparts. We show that linearly perturbed solutions may well be affected by the presence of distorted beliefs, depending on the underlying model economy. In particular, while directly affecting first‐order decision rules, near‐rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove non‐unique, pointing to a subtle form of equilibrium indeterminacy.     

An analytical perturbative solution to the Merton–Garman model using symmetries

In this paper, we introduce an analytical perturbative solution to the Merton–Garman model. It is obtained by doing perturbation theory around the exact analytical solution of a model which possesses a two-dimensional Galilean symmetry. We compare our perturbative solution of the Merton–Garman model to Monte Carlo simulations and find that our solutions perform surprisingly well for a wide range of parameters. We also show how to use symmetries to build option pricing models. Our results demonstrate that the concept of symmetry is important in mathematical finance.     

SINGULAR PERTURBATION TECHNIQUES APPLIED TO MULTIASSET OPTION PRICING

It is well known that option valuation problems with multiple-state variables are often problematic to solve. When valuing options using lattice-type techniques such as finite-difference methods, the curse of dimensionality ensures that additional-state variables lead to exponential increases in computational effort. Monte Carlo methods are immune from this curse but, despite advances, require a great deal of adaptation to treat early exercise features. Here the multiunderlying asset Black–Scholes problem, including early exercise, is studied using the tools of singular perturbation analysis. This considerably simplifies the pricing problem by decomposing the multi-dimensional problem into a series of lower-dimensional problems that are far simpler and faster to solve than the full, high-dimensional problem. This paper explains how to apply these singular perturbation techniques and explores the significant efficiency improvement from such an approach.     

POT模型中GPD“厚尾”性及金融风险测度

极端值模型是准确估计厚尾分布金融资产回报市场风险的有力工具。在越槛高峰(POT)模型中,本文对超阈值近似服从的广义Pareto分布的形状参数与厚尾性关系及其在金融风险测度中的应用进行了分析。结果表明,当0<ε≤1,y>2β/(1-ε)时,分布为厚尾分布且尾部随着形状参数的增加而变厚,此时最适合于金融资产时间序列厚尾分布风险测度和参数的极大似然估计。国内外大量的实证研究验证了上述理论并得出我国沪深股市风险特征的一些新结论。