基于跳扩散过程的欧式交换期权定价

考虑了股票价格服从带时滞泊松跳的跳扩散模型的欧式交换期权定价问题,运用无套利理论推导出期权价值微分方程,利用变换计价单位的方法,得到交换期权的显示定价公式.     

基于混合Ⅰ型删失数据的威布尔模型精确推断（英文）

威布尔分布是可靠性和寿命测试试验中常用的模型.本文中,我们考虑了基于混合Ⅰ型删失数据的威布尔模型精确推断.我们得到了威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,我们也给出了未知参数的另外几种置信区间,比如,基于近似方法的置信区间,Bootstrap置信区间.为了评价本文的方法,我们给出了一些数值模拟的结果.     

An iterative method for pricing American options under jump-diffusion models

We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou?s and Merton?s jump-diffusion models show that the resulting iteration converges rapidly.     

基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划(英文)

本文考虑基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划.得到威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,给出未知参数的另外几种置信区间,基于近似方法的置信区间.为了评价本文的方法,给出一些数值模拟的结果.且讨论了可靠性中的可接受抽样计划问题.利用参数最大似然估计的精确分布,给出一个可接受抽样计划的执行程序和数值模拟结果.     

Optimal processing rate and buffer size of a jump-diffusion processing system

In this paper, we propose a reflected jump-diffusion model for processing systems with finite buffer size. We derive an analytic expression for the total expected discounted managing cost, which facilitates finding (numerically) the optimal processing rate and buffer size that minimize the total cost. Moreover, the formula for steady-state density of the processing system is obtained.     

The exponential function rational expansion method and exact solutions to nonlinear lattice equations system

We propose an exponential function rational expansion method for solving exact traveling wave solutions to nonlinear differential-difference equations system. By this method, we obtain some exact traveling wave solutions to the relativistic Toda lattice equations system and discuss the significance of these solutions. Finally, we give an open problem.     

A jump-diffusion model for option pricing under fuzzy environments

Owing to fluctuations in the financial markets from time to time, the rate λ of Poisson process and jump sequence {V_i} in the Merton’s normal jump-diffusion model cannot be expected in a precise sense. Therefore, the fuzzy set theory proposed by Zadeh [Zadeh, L.A., 1965. Fuzzy sets. Inform. Control 8, 338-353] and the fuzzy random variable introduced by Kwakernaak [Kwakernaak, H., 1978. Fuzzy random variables I: Definitions and theorems. Inform. Sci. 15, 1-29] and Puri and Ralescu [Puri, M.L., Ralescu, D.A., 1986. Fuzzy random variables. J. Math. Anal. Appl. 114, 409-422] may be useful for modeling this kind of imprecise problem. In this paper, probability is applied to characterize the uncertainty as to whether jumps occur or not, and what the amplitudes are, while fuzziness is applied to characterize the uncertainty related to the exact number of jump times and the jump amplitudes, due to a lack of knowledge regarding financial markets. This paper presents a fuzzy normal jump-diffusion model for European option pricing, with uncertainty of both randomness and fuzziness in the jumps, which is a reasonable and a natural extension of the Merton [Merton, R.C., 1976. Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3, 125-144] normal jump-diffusion model. Based on the crisp weighted possibilistic mean values of the fuzzy variables in fuzzy normal jump-diffusion model, we also obtain the crisp weighted possibilistic mean normal jump-diffusion model. Numerical analysis shows that the fuzzy normal jump-diffusion model and the crisp weighted possibilistic mean normal jump-diffusion model proposed in this paper are reasonable, and can be taken as reference pricing tools for financial investors.     

指数Lévy跳-扩散模型下欧式期权的COS定价方法

主要研究指数Lévy形式的跳-扩散模型下欧式期权的定价问题.首先,给出了模型在均值修正等价鞅测度下的风险中性特征函数;然后,基于特征函数给出了欧式期权的傅里叶COS定价方法,并对COS方法进行修正,得到了指数Lévy形式跳-扩散模型的期权定价公式;最后,通过数值实验和实证分析检验了COS定价方法有效性,结果表明COS方...     

A market-based martingale valuation approach to optimum inventory control in a doubly stochastic jump-diffusion economy

We propose a novel market-based approach to optimum inventory control in a doubly stochastic jump-diffusion economy by modelling a commodity distributor’s inventory investment as a portfolio of forward commitments with explicit accounting of the jump-diffusion dynamics of demands, costs, and prices in open markets. We apply the robust real-asset martingale valuation methodology to derive a closed-form solution for the inventory value and a simple and intuitive optimality condition. Numerical analysis verifies this condition and demonstrates that the resulting optimum policy has robust properties in relation to the stylized effects.     

Stochastic differential portfolio games for an insurer in a jump-diffusion risk process

We discuss an optimal portfolio selection problem of an insurer who faces model uncertainty in a jump-diffusion risk model using a game theoretic approach. In particular, the optimal portfolio selection problem is formulated as a two-person, zero-sum, stochastic differential game between the insurer and the market. There are two leader-follower games embedded in the game problem: (i) The insurer is the leader of the game and aims to select an optimal portfolio strategy by maximizing the expected utility of the terminal surplus in the “worst-case” scenario; (ii) The market acts as the leader of the game and aims to choose an optimal probability scenario to minimize the maximal expected utility of the terminal surplus. Using techniques of stochastic linear-quadratic control, we obtain closed-form solutions to the game problems in both the jump-diffusion risk process and its diffusion approximation for the case of an exponential utility.     

Optimal Data Selection for Piezoelectric Material Characterization

In the simulation and design of piezoelectric transducers the exact knowledge of the entries in the material tensors - the elastic, dielectric and piezoelectric coupling coefficients - is an important prerequisite. Our task is the identification of these coefficients from indirect measurements, namely electric impedance data at different frequencies. This leads to a parameter identification problem for a system of coupled PDEs, which we solve by regularized Newton iterations. A crucial issue is the selection of frequencies at which measurements are taken. Here, we discuss the problem of choosing these frequencies in an optimal way to preserve efficiency of our identification scheme while improving reliability of the reconstruction results. For this purpose, we formulate this task as an optimization problem with PDE constraints and propose two approaches for its solution. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Possion跳—扩散模型的参数估计

受有序样品聚类思想的启发,针对期权定价模型中的Possion跳—扩散模型,提出了一种基于标的资产价格历史数据的参数估计方法,并得到了较好的结果.     

非对称Possion跳——扩散模型的参数估计

受有序样本聚类思想的启发,本文针对期权定价模型中的非对称Possion跳———扩散模型,提出了一种基于标的资产价格历史数据的参数估计方法,并得到了较好的结果。     

Runge-Kutta methods for jump-diffusion differential equations

In this paper we consider Runge-Kutta methods for jump-diffusion differential equations. We present a study of their mean-square convergence properties for problems with multiplicative noise. We are concerned with two classes of Runge-Kutta methods. First, we analyse schemes where the drift is approximated by a Runge-Kutta ansatz and the diffusion and jump part by a Maruyama term and second we discuss improved methods where mixed stochastic integrals are incorporated in the approximation of the next time step as well as the stage values of the Runge-Kutta ansatz for the drift. The second class of methods are specifically developed to improve the accuracy behaviour of problems with small noise. We present results showing when the implicit stochastic equations defining the stage values of the Runge-Kutta methods are uniquely solvable. Finally, simulation results illustrate the theoretical findings.     

基于跳扩散过程的可转换债券的定价

本文标的股票的方程采用跳扩散方程,首先规定一个跳跃的涨跌区间,这样就可以很快的找出跳跃点,我们根据跳跃点将股价聚类,然后把各个类看成是总体中抽取出来的一个样本,我们就可以估计出跳扩散方程中的所有参数.由于我们的标的股票的方程是含跳过程,因此无法找出完全保值的自融资策略,但我们可以根据风险最小化的原理给出可转换债券的价格,最后运用Monte Carlo模拟计算出了南京水运转债在0时刻的价格。     

On Quadratic g-Evaluations/Expectations and Related Analysis

This work is concerned with coupling and exponential convergence rate for a class of Markovian switching jump-diffusion processes. The processes under consideration can be thought of as a number of jump-diffusion processes modulated by a Markovian switching device. For this class of processes, we construct some order-preserving couplings. Furthermore, by virtue of the coupling results, we also provide an estimate of exponential convergence rate for the Markovian switching jump-diffusion processes without Gaussian noise.     

Master surgery scheduling with consideration of multiple downstream units

We consider a master surgery scheduling (MSS) problem in which block operating room (OR) time is assigned to different surgical specialties. While many MSS approaches in the literature consider only the impact of the MSS on operating theater and operating staff, we enlarge the scope to downstream resources, such as the intensive care unit (ICU) and the general wards required by the patients once they leave the OR. We first propose a stochastic analytical approach, which calculates for a given MSS the exact demand distribution for the downstream resources. We then discuss measures to define downstream costs resulting from the MSS and propose exact and heuristic algorithms to minimize these costs.     

Viscosity Solutions of Integro-Differential Equations and Passport Options in a Jump-Diffusion Model

We study the viscosity solutions of integro-differential Hamilton–Jacobi–Bellman equations of degenerate parabolic type. These equations are from the pricing problem for the European passport options in a jump-diffusion model. The passport option is a call option on a trading account. We discuss the mathematical model for pricing problem. We prove the comparison principle, uniqueness and convexity preserving for the viscosity solutions of related pricing equations.     

Option pricing under jump-diffusion models with mean-reverting bivariate jumps

We propose a jump-diffusion model where the bivariate jumps are serially correlated with a mean-reverting structure. Mathematical analysis of the jump accumulation process is given, and the European call option price is derived in analytical form. The model and analysis are further extended to allow for more general jump sizes. Numerical examples are provided to investigate the effects of mean-reversion in jumps on the risk-neutral return distributions, option prices, hedging parameters, and implied volatility smiles.     

Coupling for Markovian switching jump-diffusions

This work is concerned with coupling for a class of Markovian switching jump-diffusion processes. The processes under consideration can be regarded as a number of jump-diffusion processes modulated by a Markovian switching device. For this class of processes, we construct a successful coupling and an order-preserving coupling.