切换成本对线性市场投资决策影响的实物期权分析

本文基于Hotelling模型,针对一个企业在线性区域内的投资决策,考虑投资者在采用为自己作为新进入公司,为新客户使用本公司的产品付出切换成本来竞争市场的策略行为,建立需求不确定环境中的连续动态模型,应用实物期权分析方法评价投资者的投资机会价值和最优投资策略,研究切换成本对投资者投资机会的价值和投资决策的影响.本文研究结果给出了投资者在付出切换成本获得市场份额和减少成本增加投资价值之间的权衡.     

分数布朗运动环境下欧式幂期权的定价

本文主要讨论了标的资产受多个分数布朗运动影响的欧式幂期权定价问题:基于风险中性概率测度,给出了在有红利支付且无风险利率及红利率为非随机函数的情况下的两类欧式幂期权定价公式,并分别求出了涨跌欧式幂期权的平价关系.     

CIR利率模型的期权定价

本文讨论了利率服从Vasicek模型时,跳跃扩散模型下欧式期权定价问题.利用特征函数和傅立叶逆反变换,给出了这一模型下欧式看涨期权的定价公式.     

A Soft Zwitterionic Hydrogel as Potential Coating on a Polyimide Surface to Reduce Foreign Body Reaction to Intraneural Electrodes

Invasive intraneural electrodes can control advanced neural-interfaced prostheses in human amputees. Nevertheless, in chronic implants, the progressive formation of a fibrotic capsule can gradually isolate the electrode surface from the surrounding tissue leading to loss of functionality. This is due to a nonspecific inflammatory response called foreign-body reaction (FBR). The commonly used poly(ethylene glycol) (PEG)-based low-fouling coatings of implantable devices can be easily encapsulated and are susceptible to oxidative damage in long-term in vivo applications. Recently, sulfobetaine-based zwitterionic hydrogels have emerged as an important class of robust ultra-low fouling biomaterials, holding great potential to mitigate FBR. The aim of this proof-of-principle in vitro work was to assess whether the organic zwitterionic—poly(sulfobetaine methacrylate) [poly(SBMA)]—hydrogel could be a suitable coating for Polyimide (PI)-based intraneural electrodes to reduce FBR. We first synthesized and analyzed the hydrogel through a mechanical characterization (i.e., Young’s modulus). Then, we demonstrated reduced adhesion and activation of fibrogenic and pro-inflammatory cells (i.e., human myofibroblasts and macrophages) on the hydrogel compared with PEG-coated and polystyrene surfaces using cell viability assays, confocal fluorescence microscopy and high-content analysis of oxidative stress production. Interestingly, we successfully coated PI surfaces with a thin film of the hydrogel through covalent bond and demonstrated its high hydrophilicity via water contact angle measurement. Importantly, we showed the long-term release of an anti-fibrotic drug (i.e., Everolimus) from the hydrogel. Because of the low stiffness, biocompatibility, high hydration and ultra-low fouling characteristics, our zwitterionic hydrogel could be envisioned as long-term diffusion-based delivery system for slow and controlled anti-inflammatory and anti-fibrotic drug release in vivo.     

CHANGE OF NUMÉRAIRE AND AMERICAN OPTIONS

The change of numéraire technique is a standard tool in mathematical finance. We apply it to the analysis of the value and the hedging strategies of American options.

The change of numéraire is particularly powerful if the option is written on more assets and has a positively homogeneous payoff. In this case, the option writer doesn't need the riskless bond to hedge his position. We treat some examples as the Margrabe option on two stocks paying continuous dividends and the best of two assets option. Thanks to variational inequalities we are able to give numerical results for the pricing and the hedging of such a kind of American options.     

Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company’s expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.     

原棉异纤维检测系统照明光源光照度分布研究

在基于机器视觉的原棉异纤维检测系统中,选择能满足检测系统的光源和照明方案是提高系统检测率和检出率的关键,使检测对象尽可能多地显现出特征信息。选用单芯片InGaN(蓝)/YAG荧光粉型白光LED作为照明光源,采用理论计算和非成像光学设计的方法对LED阵列的光照度分布进行了研究,并根据原棉异纤维检测系统对光源光照度的具体要求,设计出了LED正方形阵列和三角形阵列两种排列方式,并利用TracePro软件对两种阵列形式进行仿真。通过比较两种阵列形式光照度分布的结果,最终选用高光照度且均匀性好的LED三角形阵列作为原棉异纤维检测系统的照明光源,满足了机器视觉成像的要求。     

Revisiting corporate growth options in the presence of state-dependent cashflow risk

Given a non-trivial market price of risk, we study the impact of state-dependent cashflow risk on the optimal investment policy and on the ensuing value of an unlevered firm that holds the option of scaling up cashflows from its assets in place upon incurring an irreversible cost. The firm’s investment decision and value are studied as a function of the market price of risk and of the degree of state dependence in cashflow risk.     

Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads

We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid–ask prices of vanilla call options in the underlying securities. We show that this semi-infinite problem can be recast as a linear program whose size is linear in the input data size. These developments advance previous related results, and enhance the practical value of static-arbitrage bounds as a pricing technique by taking into account the presence of bid–ask spreads. We illustrate our results by computing upper bounds on the price of a DJX basket option. The MATLAB code used to compute these bounds is available online at www.andrew.cmu.edu/user/jfp/arbitragebounds.html.     

An ETD Crank‐Nicolson method for reaction‐diffusion systems

A novel Exponential Time Differencing Crank‐Nicolson method is developed which is stable, second‐order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case, we employ a positivity‐preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a wide variety of examples, including chemotaxis and exotic options with transaction cost. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012