Time-changed geometric fractional Brownian motion and option pricing with transaction costs

This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black–Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.     

An integrated toll and ramp control methodology for dynamic freeway congestion management

This paper investigates an integrated freeway traffic management system, which coordinates both dynamic toll pricing and ramp control strategies for the purpose of dynamic freeway congestion management. The proposed integrated dynamic toll-ramp control methodology is built mainly on the principles of stochastic optimal control approaches, involving two developmental procedures. First, through detector configurations and system specification, a discrete-time nonlinear stochastic system is formulated to characterize the time-varying relationships of system states, control variables, and traffic data. Then, by employing the extended Kalman filtering technology, a stochastic optimal control based algorithm is proposed to execute the integrated dynamic toll and ramp control mechanism. With the aid of the Paramics microscopic traffic simulator, numerical studies under various simulated freeway congestion scenarios are conducted. Corresponding numerical results demonstrate the applicability of the proposed methodology in response to diverse freeway traffic congestion phenomena, and its relative advantages in improving both the average travel time and hourly throughputs by 16.4% and 16.5%, respectively.     

考虑保质期的非即时易腐品最优订购与定价决策

针对有保质期约束的非即时易腐品,零售商可以在产品非腐败阶段和腐败阶段进行差异化定价来调整市场需求。即零售商可以调整产品非腐败阶段的定价策略,使得非即时易腐品在进入腐败阶段之前全部售出;或者在产品腐败阶段降低零售价格以刺激市场需求。因此,在需求依赖价格的假设下,本文研究了零售商关于有保质期约束的非即时易腐品的最优订购与定价决策。通过分析零售商单位时间利润函数的理论性质,得到了零售商的最优订购与定价策略。基于线性和指数型两种需求函数形式进行数值算例,可以发现针对保质期较长或者非腐败阶段较长的易腐品,零售商会延长订货周期来增加销售收入。特别是在指数型需求函数情境下,当市场需求与零售价格高度相关时,零售商更有意愿降价来刺激销量,从而使得易腐品在非腐败阶段内销售完毕。     

Sentiment lost: the effect of projecting the pricing kernel onto a smaller filtration set

Abstract

This paper provides a theoretical analysis on the impacts of using a suboptimal information set for the estimation of the pricing kernel and, more in general, for the validity of the fundamental theorems of asset pricing. While inferring the risk-neutral measure from options data provides a naturally forward-looking estimate, extracting the real world measure from historical returns is only partially informative, thus suboptimal with respect to investors’ future beliefs. As a consequence of this disalignment, the two measures no longer share the same nullset, thus distorting the investors’ risk premium and the validity of the pricing measure. From a probabilistic viewpoint, the missing beliefs are totally unaccessible stopping times on the coarser filtration set, so that an absolutely continuous strict local martingale, once projected on it, becomes continuous with jumps. Some empirical examples complete the paper.     

不同价格水平下排队策略研究

在M/M/1排队中引入了不同的服务价格,基于"收益-成本"结构,以顾客和企业均追求利益最大化为出发点,在两种不可见情形下,研究了顾客均衡策略行为和企业最优服务定价决策,通过数值模拟,描述了休假期服务价格对顾客均衡策略的影响,以及几乎不可见情况下休假期服务价格对企业收益的作用和完全不可见情况下休假期服务价格随潜在到达率的变化情况,以及当企业获得最大收益时,正常工作期和休假期服务价格的关系.     

基于不同融资方式的双渠道供应链定价决策

针对由一个制造商和一个有资金约束零售商组成的双渠道供应链系统,利用Stackelberg博弈模型,研究零售商分别选择银行贷款和延迟支付解决资金约束问题时,不同定价方案中制造商和零售商的最优决策,分析零售渠道市场份额以及融资利率对决策结果的影响。研究表明:零售商的资金不足不会改变各参与方最优决策随零售渠道市场份额的变化趋势。在双渠道不统一定价方案下,若选择银行贷款,只有零售渠道市场份额较小且利率较高时,直销价格随利率的增加而增加;若申请延迟支付,零售价格和直销价格不受利率影响。在双渠道统一定价方案下,销售价格只有在零售渠道市场份额较低时随银行贷款利率的增加而增加,与延迟支付利率无关。     

A stable local radial basis function method for option pricing problem under the Bates model

We propose a local mesh‐free method for the Bates–Scott option pricing model, a 2D partial integro‐differential equation (PIDE) arising in computational finance. A Wendland radial basis function (RBF) approach is used for the discretization of the spatial variables along with a linear interpolation technique for the integral operator. The resulting set of ordinary differential equations (ODEs) is tackled via a time integration method. A potential advantage of using RBFs is the small number of discrete equations that need to be solved. Computational experiments are presented to illustrate the performance of the contributed approach.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It\^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment. According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

Optimal uniform error estimates for moving least‐squares collocation with application to option pricing under jump‐diffusion processes

In this study, we derive optimal uniform error bounds for moving least‐squares (MLS) mesh‐free point collocation (also called finite point method) when applied to solve second‐order elliptic partial integro‐differential equations (PIDEs). In the special case of elliptic partial differential equations (PDEs), we show that our estimate improves the results of Cheng and Cheng (Appl. Numer. Math. 58 (2008), no. 6, 884–898) both in terms of the used error norm (here the uniform norm and there the discrete vector norm) and the obtained order of convergence. We then present optimal convergence rate estimates for second‐order elliptic PIDEs. We proceed by some numerical experiments dealing with elliptic PDEs that confirm the obtained theoretical results. The article concludes with numerical approximation of the linear parabolic PIDE arising from European option pricing problem under Merton's and Kou's jump‐diffusion models. The presented computational results (including the computation of option Greeks) and comparisons with other competing approaches suggest that the MLS collocation scheme is an efficient and reliable numerical method to solve elliptic and parabolic PIDEs arising from applied areas such as financial engineering.     

考虑广告投放的不对称竞争企业定价策略研究

针对非对称双寡头竞争企业中广告投放以及定价策略等问题,本文首先依据市场细分构建了统一定价和差异化定价模型;其次,以定价模型为基础,针对转化者市场是否存在偏好,构建了不同情境下的效益模型,并利用博弈论确定不同阶段的均衡结果,通过对均衡结果的分析,得出广告成本以及竞争市场的差异化程度对均衡结果的影响,最后利用数值分析验证结果的有效性。