Reflected BSDE Driven by a Lévy Process

In this paper, we study the reflected solution of one-dimensional backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove the existence and uniqueness of the solution using a penalization method combined with Snell envelope theory.      

考虑预付定金和退货的SMPEs产品定价与优化策略

借鉴中小制造型企业(SMPEs)在线渠道预售模式,考虑市场中存在预付订金和不预付订金的顾客,并将其退货情况引入到生产商利润表达式中,构建确定性和随机性市场需求下的SMPEs产品销售利润最大化模型,推导生产商产品最优定价的解析解;对比两种销售模式的利润,得到了生产商选择不同销售策略的条件。进一步考虑预付定金的产品数量、预交定金比例、退货数量是关于价格折扣敏感的情况,采用拉格朗日乘子法对生产商产品定价及优化问题进行研究,分析求得生产商销售策略(产品定价和价格折扣)的近似最优解。最后,通过数值算例对研究结论进行了验证并给出经济学解释。     

不透明销售的顾客退货政策选择

本文探讨从事不透明销售的零售商对顾客退货政策的选择问题。分别针对零售商垄断和竞争两种市场情况,建立不透明零售商与其它供应链成员(制造商或普通零售商)之间的博弈模型,获得唯一均衡解;对均衡结果进行结构化分析,给出不透明销售方式下采用全额退款政策的判别条件;针对均衡结果,分析零售商垄断情况下产品不透明参数的最优设计,以及零售商竞争情况下的市场分化情况;鉴于净残值参数在退货政策选择中的决定性作用,本文进一步探讨了净残值为正时全额退款政策对各参与方利润及产品需求和价格的影响,分析了净残值在其中的作用机理。本研究能够为不透明零售商制定退货政策和价格以及其它供应链成员制定相关决策提供支持。     

消费者异质性下基础产品及其附加品的供应链定价策略研究

建立一个由制造商和销售商组成的二级供应链模型,在销售商向消费者销售制造商基础产品的同时提供可选附加品的供应链多产品定价背景下研究了制造商及销售商的定价策略。以消费者对附加品价值增值存在的异质性将基础产品及其附加品的消费市场细分为基础产品单独消费市场及产品共同消费市场。基于市场细分比例以及附加品价值增值程度,讨论了不同条件下制造商及销售商的定价策略以及所形成的供应链定价均衡,分析了产品定价均衡与市场细分比例、附加品价值增值程度之间的关系。     

Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios

We derive in closed form distribution free lower bounds and optimal subreplicating strategies for spread options in a one-period static arbitrage setting. In the case of a continuum of strikes, we complement the optimal lower bound for spread options obtained in [Rapuch, G., Roncalli, T., 2002. Pricing multiasset options and credit derivatives with copula, Credit Lyonnais, Working Papers] by describing its corresponding subreplicating strategy. This result is explored numerically in a Black-Scholes and in a CEV setting. In the case of discrete strikes, we solve in closed form the optimization problem in which, for each asset S₁ and S₂, forward prices and the price of one option are used as constraints on the marginal distributions of each asset. We provide a partial solution in the case where the marginal distributions are constrained by two strikes per asset. Numerical results on real NYMEX (New York Mercantile Exchange) crack spread option data show that the one discrete lower bound can be far and also very close to the traded price. In addition, the one strike closed form solution is very close to the two strike.     

Incomplete financial markets and contingent claim pricing in a dual expected utility theory framework

This paper investigates the price for contingent claims in a dual expected utility theory framework, the dual price, considering arbitrage-free financial markets. A pricing formula is obtained for contingent claims written on n underlying assets following a general diffusion process. The formula holds in both complete and incomplete markets as well as in constrained markets. An application is also considered assuming a geometric Brownian motion for the underlying assets and the Wang transform as the distortion function.     

A Markov-modulated model for stocks paying discrete dividends

We extend the model in [Korn, R., Rogers, L.C.G., 2005. Stock paying discrete dividends: modelling and option pricing. Journal of Derivatives 13, 44–49] for (discrete) dividend processes to incorporate the dependence of assets on the market mode or the state of the economy, where the latter is modeled by a hidden finite-state Markov chain. We then derive the resulting dynamics of the stock price and various option-pricing formulae. It turns out that the stock price jumps not only at the time of the dividend payment, but also when the underlying Markov chain jumps.     

Risk-sensitive dynamic pricing for a single perishable product

We show that the monotone structures of dynamic pricing for a single perishable product under risk-neutrality are preserved under risk-sensitivity with the additive general utility and atemporal exponential utility functions. We also show that the optimal price is decreasing over the degree of risk-sensitivity under the exponential class of both additive and atemporal utility functions.     

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.