Infinite-Dimensional Black-Scholes Equation with Hereditary Structure

This paper considers the option pricing problem for contingent claims of the European type in a (B,S)-market in which the stock price and the asset in the riskless bank account both have hereditary structures. The Black-Scholes equation for the classical option pricing problem is generalized to an infinite-dimensional equation to include the effects of time delay in the evolution of the financial market as well as a very general payoff function. A computational algorithm for the solution is also obtained via a double sequence of polynomials of a certain bounded linear functional on a Banach space and the time variable.     

离散时间不完全金融市场中未定权益的定价

对一类连续时间不完全市场（其中的股票价格由Brown运动驱动），ElKarouiandQuenez[1]讨论了一般的不可达未定权益的定价问题．本文利用FollmerandKabanov[2]建立的分解定理，证明[1]中关于买方与卖方价格过程的结果与方法适用于一般的离散时间不完全金融市场（定理1）．特别，关于买方与卖方价格我们给出另一种合理的解释（定理3）．     

具有跳跃特征的资产价格过程的期权定价模型研究

资产价格具有跳跃特征时，衍生于该资产的期权就不能利用传统的Black-Schoels公式进行定价。本主要研究基于Poisson过程和固定跳跃Merton模型的期权定价与风险对冲问题，利用e-套利定价法，得到期权的风险对冲策略所满足的偏微分方程和近似期权定价。     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

Stochastic model for market stocks with floors

We present a model to describe the stochastic evolution of stocks that show a strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general securities that pay dividends at a continuous rate and earn a terminal payoff at maturity T is solved via the martingale probability approach.     

Option Pricing and Hedging under a Markov Switching Lévy Process Model

In this paper,we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging.In this model,the market interest rate,the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process.We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure.The option price using this model is obtained by the Fourier transform method.We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.     

Unifying pricing formula for several stochastic volatility models with jumps

In this paper, we introduce a unifying approach to option pricing under continuous‐time stochastic volatility models with jumps. For European style options, a new semi‐closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro‐differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log‐normal and a log‐uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yan and Hanson, respectively. The comparison of existing and newly proposed option pricing formulas with respect to time efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out‐of‐the money contracts. Copyright © 2017 John Wiley & Sons, Ltd.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.