再装股票期权的Esscher变换定价

近年来,公司为了吸引和激励股票的执行者而引入了一系列的非传统期权.本文将讨论其中的一种:再装期权,运用Esscher变换给出了再装期权(只装一次)的闭式解,并提供了数值计算的例子,为实践者提供了理论上的参考价格.     

Representing Discrete Events in System Dynamics Models: A Theoretical Application to Modelling Coal Production

The paper begins with the suggestion that simulation modelling has traditionally been divided into two separate types-open-loop discrete-event based analysis and closed-loop continuous modelling. Separate simulation packages have been evolved for meeting these needs.There are, however, important managerial problems where the discrete and feedback processes are both present and are both significant, and they pose a modelling dilemma. It is shown that the dilemma can be resolved, without the use of hybrid languages, by using the random processes and very flexible logical operator facilities in DYSMAP in a novel way to create discrete events. This is demonstrated by a theoretical application within the coal mining industry.     

A new discrete mechanics approach to swing-up control of the cart-pendulum system

This paper develops a new swing-up control method for the cart-pendulum system via discrete mechanics. The swing-up control law consists of two parts: the swing-up stage and the stabilization one. In the swing-up stage, we use a controller based on a discrete Lyapunov function and it can swing up the pendulum. Then, in the stabilization stage, we utilize a stabilizing controller based on the linearized system and discrete-time optimal regulator theory. In addition, transformation methods from discrete control inputs into continuous zero-order hold inputs are introduced. From some simulation results, we can confirm that the cart-pendulum system is swung up and stabilized by our new method.     

Gas Supply and Storage Planning: A Simulation Approach

This paper describes the problems faced by a region of British Gas in forecasting daily gas demand and gas storage requirements. The discrete simulation approach is used to model the gas supply system. The paper discusses how the relationships and interactions between the various parts of the system may be determined by using the simulation program which has been developed and implemented.     

Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry

The underlying time framework used is one of the major differences in the basic structure of mathematical programming formulations used for production scheduling problems. The models are either based on continuous or discrete time representations. In the literature there is no general agreement on which is better or more suitable for different types of production or business environments. In this paper we study a large real-world scheduling problem from a pharmaceutical company. The problem is at least NP-hard and cannot be solved with standard solution methods. We therefore decompose the problem into two parts and compare discrete and continuous time representations for solving the individual parts. Our results show pros and cons of each model. The continuous formulation can be used to solve larger test cases and it is also more accurate for the problem under consideration.     

High-Dimensional Mixed Graphical Models

While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models for datasets with both continuous and discrete variables (mixed data), which are common in many scientific applications. We propose a novel graphical model for mixed data, which is simple enough to be suitable for high-dimensional data, yet flexible enough to represent all possible graph structures. We develop a computationally efficient regression-based algorithm for fitting the model by focusing on the conditional log-likelihood of each variable given the rest. The parameters have a natural group structure, and sparsity in the fitted graph is attained by incorporating a group lasso penalty, approximated by a weighted lasso penalty for computational efficiency. We demonstrate the effectiveness of our method through an extensive simulation study and apply it to a music annotation dataset (CAL500), obtaining a sparse and interpretable graphical model relating the continuous features of the audio signal to binary variables such as genre, emotions, and usage associated with particular songs. While we focus on binary discrete variables for the main presentation, we also show that the proposed methodology can be easily extended to general discrete variables.     

Inventory control as a discrete system control for the fixed-order quantity system

This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.     

Parallel simulation of individual-based, physiologically structured population models

A general scheme for parallel simulation of individual-based, structured population models is proposed. Algorithms are developed to simulate such models in a parallel computing environment. The simulation model consists of an individual model and a population model that incorporates the individual dynamics. The individual model is a continuous time representation of organism life history for growth with discrete allocations for reproductive processes. The population model is a continuous time simulation of a nonlinear partial differential equation of extended McKendrick-von Foerster-type.

As a prototypical example, we show that a specific individual-based, physiologically structured model for Daphnia populations is well suited for parallelization, and significant speed-ups can be obtained by using efficient algorithms developed along our general scheme. Because the parallel algorithms are applicable to generic structured populations which are the foundation for populations in a more complex community or food-web model, parallel computation appears to be a valuable tool for ecological modeling and simulation.     

Floquet theory for a Volterra integro-dynamic system

In this paper, we study periodic linear Volterra systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We discuss the relationship between the solution of the Volterra integro-dynamic system and the limiting equation of the corresponding system. We also develop integrability conditions of the resolvent of Volterra integro-dynamic systems.     

高管个人特征对股权激励模式选择的影响研究

上市公司股权激励模式的选择问题一直受社会各界关注。本文利用2006年到2017年期间实施股权激励的上市公司数据,研究了高管个人特征如何对股权激励模式的选择产生影响。结果表明,被激励高管的个人特征如高管年龄、任期、学历与社会资本显著影响公司股权激励模式的选择,年龄越大、任期越久、学历越高、社会资本越丰富的高管,公司更倾向选择限制性股票激励模式;男性高管越多的公司,越倾向选择股票期权激励模式,然而性别对其影响并不显著。本文在经过一系列的稳健性和内生性检验后,研究结论依然成立。本文研究结果丰富了股权激励相关理论,并为上市公司科学合理地选择股权激励模式提供参考。     

A Markov chain Monte Carlo Expectation Maximization Algorithm for Statistical Analysis of DNA Sequence Evolution with Neighbor-Dependent Substitution Rates

The evolution of DNA sequences can be described by discrete state continuous time Markov processes on a phylogenetic tree. We consider neighbor-dependent evolutionary models where the instantaneous rate of substitution at a site depends on the states of the neighboring sites. Neighbor-dependent substitution models are analytically intractable and must be analyzed using either approximate or simulation-based methods. We describe statistical inference of neighbor-dependent models using a Markov chain Monte Carlo expectation maximization (MCMC-EM) algorithm. In the MCMC-EM algorithm, the high-dimensional integrals required in the EM algorithm are estimated using MCMC sampling. The MCMC sampler requires simulation of sample paths from a continuous time Markov process, conditional on the beginning and ending states and the paths of the neighboring sites. An exact path sampling algorithm is developed for this purpose.     

Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy

The paper consists of two parts. In the first part, we prove a noncommutative analog of the Riesz(— Markov—Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space. In the second part, using this result, we prove a weak version of a Burnside type theorem on twisted conjugacy for arbitrary discrete groups.     

Modelling and Verification using Linear Hybrid Automata -- a Case Study

This paper discusses the use of hybrid automata to specify and verify embedded distributed systems, that consist of both discrete and continuous components. The basis of the evaluation is an automotive control system, which controls the height of an automobile by pneumatic suspension. It has been proposed by BMW AG as a case study taken from a current industrial development. Essential parts of the system have been modelled as hybrid automata and for appropiate ions several safety properties have been verified. The verification has been performed using HYTECH, a symbolic model checker for linear hybrid automata. The paper discusses the general appropiateness of hybrid automata to specify hybrid systems as well as advantages and drawbacks of the applied model-checking techniques.     

Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials

We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.     

Dynamical behaviors of a discrete two-dimensional competitive system exactly driven by the large centre

In this paper, a new discrete large-sub-center system is obtained by using the Euler and nonstandard discretization methods for the corresponding continuous system. It is surprised that all dynamic behaviors of the discrete system are exactly driven by the large-center equation, for example, the stabilities, the bifurcations, the period-doubling orbits, and the chaotic dynamics, etc. Additionally, the global asymptotical stability, the existence of exact 2-periodic solutions, the flip bifurcation theorem, and the invariant set of the sub-center equation is also given. These results reveal far richer dynamics of the discrete model compared with the continuous model. Through numerical simulation, we can observe some complex dynamic behaviors, such as period-doubling cascade, periodic windows, chaotic dynamics, etc. Especially, our theoretical results are also showed by those numerical simulations.     

Hybrid observer design for linear switched system via Differential Petri Nets

The aim of this paper is to propose a hybrid observer design for linear switched systems modelled either via Differential Petri Nets (DPN) or via Timed Differential Petri Nets (TDPN). The switched systems, herein, considered are characterized by switching laws that can depend on the continuous states or on both of a given dwell time and the continuous states. In addition, the structure of the proposed observers is based on a discrete observer and a continuous observer on interaction. The discrete observer reconstructs the discrete mode, by estimating both of the discrete marking and the firing vector. Once, the active mode is obtained, the continuous states are estimated. Finally, the outputs of the continuous observer are used to update the marking and the firing vector. At the end of the paper, several simulation results are presented to illustrate the proposed approach.     

Multilevel hybrid split-step implicit tau-leap

In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been shown to be more relevant than continuous state-space and deterministic ones. In systems characterized by having simultaneously fast and slow timescales, existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap (explicit-TL) method, can be very slow. Implicit approximations have been developed to improve numerical stability and provide efficient simulation algorithms for those systems. Here, we propose an efficient Multilevel Monte Carlo (MLMC) method in the spirit of the work by Anderson and Higham (SIAM Multiscal Model. Simul. 10(1), 2012). This method uses split-step implicit tau-leap (SSI-TL) at levels where the explicit-TL method is not applicable due to numerical stability issues. We present numerical examples that illustrate the performance of the proposed method.     

The Spectra of Small Oscillations of Thin Disk Galactic Models

This paper gives a survey of the spectral properties of the frequencies of small oscillations, both in and perpendicular to their plane, of cold thin disk galactic models. The spectra can have discrete and continuous parts, with two quite distinct types of continua arising. One type occurs with both kinds of oscillation when the density at the outer edge of the disk becomes sufficiently rarified. It is associated with rapid fluctuations in the outer region. The other type of continuum occurs for non-axisymmetric oscillations in the plane of non-uniformly rotating disks. Some significant discrete oscillations of fundamental type are found that exist in addition to the various continua.     

Investigating communication and step-size behaviour for co-simulation of hybrid physical systems

This paper discusses the method of cooperative simulation of discrete and continuous models with the Building Controls Virtual Test Bed, a software environment that allows coupling different simulation programs. In the course of a project aiming the energy optimization in cutting factories, models of machines of differing complexity and a building containing them have to be implemented to further simulate the thermal processes. Since all partial models require individual modelling approaches, solver time steps, solvers or even simulators, the method of co-simulation is considered. The partial models will be implemented with Modelica, MATLAB, Simulink and Simscape and accessed with the co-simulation tool BCVTB. The simulation results show that this method of co-simulation can be sufficient for the needs of describing thermal systems with large time constants but has to be found insufficient for simulations requiring high accuracy and variable step solvers in the overall simulation.