连续红利支付在跳扩散模型下的再装期权的定价

本文在连续时间支付红利,且股票价格服从Poisson跳-扩散过程的假设下,建立股票价格模型,并应用保险精算法给出一类奇异期权—再装期权再装一次情况下的定价公式.     

Optimal pricing in a diffusion model with concave price-dependent market potential

Using optimal control theory, a diffusion model of new product acceptance is studied. We consider a profit-maximizing firm faced with the problem of determining its optimal pricing policy under the assumption that the total market potential is a concave decreasing function of price. For an infinite planning horizon it is shown by phase portrait analysis that the optimal price is steadily increasing and converging to a saddle point equilibrium.     

双指数跳扩散模型下奇异期权的定价

在双指数跳扩散模型下,利用已建立的欧式期权定价公式讨论了三种常见的奇异期权——简单任选期权、上限型买权和滞后付款期权的期权定价,得到了这些期权定价的解析公式.这是对双指数跳扩散模型期权定价的补充.     

A continuous-time dynamic pricing model knowing the competitor’s pricing strategy

In this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy. We establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly. We assume that customers arrive to purchase tickets in accordance with a geometric Brownian motion. We derive an explicit closed-form expression for an optimal pricing policy to maximize the expected revenue. It is shown that when the competitor adopts a static pricing policy, dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy. Moreover, we show that the size of the reduction in the expected revenue depends on the competitor’s pricing strategy. Numerical results are presented to illustrate the dynamic pricing policy.     

股票价格服从跳-扩散过程的下降敲出买入期权定价模型

本文讨论了一种新型期权-下降敲出买入期权定价问题.建立了由Possion跳-扩散过程驱动下的股票价格行为模型.在此模型下,推导出一种欧式下降敲出买入期权的定价公式.     

Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.     

股价遵循分数跳扩散的混合型双标的两值期权定价

应用风险中性定价原理,研究标的股价服从分数跳扩散过程的混合型双标的两值期权的定价问题,并得出定价公式,并与股价服从标准布朗运动的定价公式做出比较分析.     

离散时间跳-扩散过程的期权定价

本文运用 Cox、Ross和 Rubinstein的方法 ,建立了股票价格离散时间的跳 -扩散模型 ,通过无套利理论推导出离散时间的欧式期权和美式期权定价公式     

A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

On the causality of real‐valued semigroups and diffusion

In this paper, we show that a process modeled by a strongly continuous real‐valued semigroup (that has a space convolution operator as infinitesimal generator) cannot satisfy causality. We present and analyze a causal model of diffusion that satisfies the semigroup property at a discrete set of time points and that is in contrast to the classical diffusion model not smooth. More precisely, if v denotes the concentration of a substance diffusing with constant speed, then v is continuous, but its time derivative is discontinuous at the discrete set M of time points. Furthermore, we show that diffusion with constant speed satisfies an inhomogeneous wave equation with a time dependent coefficient. Copyright © 2011 John Wiley & Sons, Ltd.     

Polynomial diffusion models for life insurance liabilities

In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model can be used to guarantee not only the positivity of the OIS short rate and the mortality intensity, but also the possibility of approximating both pricing formula and hedging strategy of a large class of life insurance products by explicit formulas.     

幂效用函数的无差别定价和套期保值

研究了多维扩散模型幂效用函数的无差别定价和套期保值.通过动态规划方法得到了未定权益的无差别定价和套期保值策略.并证明了无差别定价与风险厌恶指数无关的.     

Optimal normative policies for marketing of products with limited availability

We develop optimal normative policies for pricing and advertising of products with limited availability by including the traditional product diffusion parameters (Bass, 1969)–innovation and imitation, and the scarcity effects generated due to limited product availability (Swami and Khairnar, 2003). Using optimal control methodology, our pricing policy results suggest that a profit-maximizing firm gradually increases the price as the sales approach the product availability. The optimal normative advertising policy recommends gradually decreasing the expenditure on the awareness advertising and increasing the expenditure on the availability advertising as the product diffusion progresses. These results are illustrated with suitable numerical examples.     

Coupling and option price comparisons in a jump-diffusion model

In this paper, we examine the dependence of option prices in a general jump-diffusion model on the choice of martingale pricing measure. Since the model is incomplete, there are many equivalent martingale measures. Each of these measures corresponds to a choice for the market price of diffusion risk and the market price of jump risk. Our main result is to show that for convex payoffs, the option price is increasing in the jump-risk parameter. We apply this result to deduce general inequalities, comparing the prices of contingent claims under various martingale measures, which have been proposed in the literature as candidate pricing measures.

Our proofs are based on couplings of stochastic processes. If there is only one possible jump size then we are able to utilize a second coupling to extend our results to include stochastic jump intensities.     

Optimal stopping of switching diffusions with state dependent switching rates

This paper is concerned with a continuous-time and infinite-horizon optimal stopping problem in switching diffusion models. In contrast to the assumption commonly made in the literature that the regime-switching is modeled by an independent Markov chain, we consider in this paper the case of state-dependent regime-switching. The Hamilton–Jacobi–Bellman (HJB) equation associated with the optimal stopping problem is given by a system of coupled variational inequalities. By means of the dynamic programming (DP) principle, we prove that the value function is the unique viscosity solution of the HJB system. As an interesting application in mathematical finance, we examine the problem of pricing perpetual American put options with state-dependent regime-switching. A numerical procedure is developed based on the DP approach and an efficient discrete tree approximation of the continuous asset price process. Numerical results are reported.     

On semimartingale diffusions and stochastic differential equations

Given a regular diffusion X on the real axis which is a semimartingale we describe the semimartingale decomposition of X. We then give necessary and sufficient conditions in terms of the scale and the speed measure for X being a solution of an Ito type stochastic differential equation driven by a Wiener process and with classical drift or a drift term involving the local time of X. A regular diffusion is also characterized as unique solution of a certain martingale problem. Finally we discuss an example related to skew Brownian motion     

基于双指数跳扩散模型的可转换债券定价

本文研究列维系统中的可转换债券的定价．我们证明了可转换债券中的隐含call部分的价值可转换为一个美式put．最后我们给出了在标的服从双指数跳扩散过程时隐含call的价值近似表达．     

Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion

In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.     

最优投资消费策略

投资消费问题是数理金融中的一个主要问题,Merton在假设股票价格过程为扩散过程的情形下,给出了最优投资消费策略的显式解,本在股份价格过程为跳－扩散过程的情形下,讨论了最优投资消费策略问题,得到了最优投资消费策略的偏微分方程。     

批量购买下免费商品赠送对新产品扩散的影响

在非耐用品的购买过程中,批量购买的消费行为较为普遍。本文基于Bass模型,将批量购买看作一个扩散过程,建立批量购买下含免费商品的产品扩散模型;然后在扩散模型中引入重复购买和价格策略等因素的影响,构建了优化模型群。对不同购买方式下的免费商品赠送进行仿真分析,同时对模型中重要参数进行优化后分析,计算分析表明:和单量购买情形一致,当存在批量购买时,免费商品的赠送同样会加快产品的扩散速度,但值得赠送更多的免费商品以达到利润最大化。消费者的批量购买量越大,就越有必要赠送更多的免费商品来让消费者了解该产品,甚至对每个消费者发放免费商品。同时,通过对赠送时期的对比分析,发现只有在产品引入初期赠送最佳,形成了“首期赠送效应”。最后,给出了参数对免费商品赠送水平的影响范围与趋势。