Biological Jumping Mechanism Analysis and Modeling for Frog Robot

This paper presents a mechanical model of jumping robot based on the biological mechanism analysis of frog. By biological observation and kinematic analysis the frog jump is divided into take-offphase, aerial phase and landing phase. We find the similar trajectories of hindlimb joints during jump, the important effect of foot during take-off and the role of forelimb in supporting the body. Based on the observation, the frog jump is simplified and a mechanical model is put forward. The robot leg is represented by a 4-bar spring/linkage mechanism model, which has three Degrees of Freedom （DOF） at hip joint and one DOF （passive） at tarsometatarsal joint on the foot. The shoulder and elbow joints each has one DOF for the balancing function of arm. The ground reaction force of the model is analyzed and compared with that of frog during take-off. The results show that the model has the same advantages of low likelihood of premature lift-off and high efficiency as the frog. Analysis results and the model can be employed to develop and control a robot capable of mimicking the jumping behavior of frog.

Modeling of Carrier-based Aircraft Ski Jump Take-off Based on Tensor

A general mathematical model of carrier-based aircraft ski jump take-off is derived based on tensor. The carrier, the aircraft body and the movable parts of the landing gears are treated as independent entities. These entities are assembled into a multi-rigid-body system with flexible links. Dynamical equations of each entity are derived on the basis of the Newton law and the Euler transformation. Using the invariance property of the tensor, the dynamical and kinematical equations are converted to tensor forms which are invariant under time-dependent coordinate transformations. Then the tensor-formed equations are expressed by the matrix operation. Differential equation group of the matrix form is formulated for the programming. The closure of the model is discussed, and the simulation results are given.

WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL

Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

Experimental investigation on single person's jumping load model

This paper presents a modified half-sine-squared load model of the jumping impulses for a single person. The model is based on a database of 22,921 experimentally measured single jumping load cycles from 100 test subjects. Threedimensional motion capture technology in conjunction with force plates was employed in the experiment to record jumping loads. The variation range and probability distribution of the controlling parameters for the load model such as the impact factor, jumping frequency and contact ratio, are discussed using the experimental data. Correlation relationships between the three parameters are investigated. The contact ratio and jumping frequency are identified as independent model parameters, and an empirical frequency-dependent function is derived for the impact factor. The feasibility of the proposed load model is established by comparing the simulated load curves with measured ones, and by comparing the acceleration responses of a single-degree-of-freedom system to the simulated and measured jumping loads. The results show that a realistic individual jumping load can be generated by the proposed method. This can then be used to assess the dynamic response of assembly structures.

Valuing Credit Default Swap under a double exponential jump diffusion model

This paper discusses the valuation of the Credit Default Swap based on a jump market, in which the asset price of a firm follows a double exponential jump diffusion process, the value of the debt is driven by a geometric Brownian motion, and the default barrier follows a continuous stochastic process. Using the Gaver-Stehfest algorithm and the non-arbitrage asset pricing theory, we give the default probability of the first passage time, and more, derive the price of the Credit Default Swap.

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

PRICING EUROPEAN OPTION IN A DOUBLE EXPONENTIAL JUMP-DIFFUSION MODEL WITH TWO MARKET STRUCTURE RISKS AND ITS COMPARISONS

Using Fourier inversion transform, P.D.E. and Feynman-Kac formula, the closedform solution for price on European call option is given in a double exponential jump-diffusion model with two different market structure risks that there exist CIR stochastic volatility of stock return and Vasicek or CIR stochastic interest rate in the market. In the end, the result of the model in the paper is compared with those in other models, including BS model with numerical experiment. These results show that the double exponential jump-diffusion model with CIR-market structure risks is suitable for modelling the real-market changes and very useful.

Distributed Model Predictive Control with Actuator Saturation for Markovian Jump Linear System

This paper is concerned with the distributed model predictive control (MPC) problem for a class of discrete-time Markovian jump linear systems (MJLSs) subject to actuator saturation and polytopic uncertainty in system matrices. The global system is decomposed into several subsystems which coordinate with each other. A set of distributed controllers is designed by solving a min-max optimization problem in terms of the solutions of linear matrix inequalities (LMIs). An iterative algorithm is developed to achieve the online computation. Finally, a simulation example is employed to show the effectiveness of the proposed algorithm. © 2014 Chinese Association of Automation.

Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model

This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.

Pricing VIX options in a 3/2 plus jumps model

This paper proposes and makes a study of a new model(called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests.The results show that the models are capable of fitting the market price while generating positive volatility skew.

A Study of Aviation Weapon Equipment Maintenance Based on the Semi-Markov Model

Based on the Semi-Markov mathematical description, the multiple states of maintenance processes for aviation weapon equipment are studied. Six kinds of maintenance states are determined and the Semi-Markov model of the maintenance process is given. According to maintenance characteristic, the multiple states maintenance processes are divided into the wait, use and alternate stages. Through using the mathematical model for the different stages, the probability in different states and effective index on different stages are obtained. These results are available to the maintenance practice.

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option;numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

Risk Identification based on Hidden Semi-Markov Model in Smart Distribution Network

The smart distribution system is the critical part of the smart grid, which also plays an important role in the safe and reliable operation of the power grid. The self-healing function of smart distribution network will effectively improve the security, reliability and efficiency, reduce the system losses, and promote the development of sustainable energy of the power grid. The risk identification process is the most fundamental and crucial part of risk analysis in the smart distribution network. The risk control strategies will carry out on fully recognizing and understanding of the risk events and the causes. On condition that the risk incidents and their reason are identified, the corresponding qualitative / quantitative risk assessment will be performed based on the influences and ultimately to develop effective control measures. This paper presents the concept and methodology on the risk identification by means of Hidden Semi-Markov Model (HSMM) based on the research of the relationship between the operating characteristics/indexes and the risk state, which provides the theoretical and practical support for the risk assessment and risk control technology.

Noncooperative Model Predictive Game With Markov Jump Graph

In this paper,the distributed stochastic model predictive control(MPC)is proposed for the noncooperative game problem of the discrete-time multi-player systems(MPSs)with the undirected Markov jump graph.To reflect the reality,the state and input constraints have been considered along with the external disturbances.An iterative algorithm is designed such that model predictive noncooperative game could converge to the socalledε-Nash equilibrium in a distributed manner.Sufficient conditions are established to guarantee the convergence of the proposed algorithm.In addition,a set of easy-to-check conditions are provided to ensure the mean-square uniform bounded stability of the underlying MPSs.Finally,a numerical example on a group of spacecrafts is studied to verify the effectiveness of the proposed method.

Dynamic assets allocation based on market microstructure model with variable-intensity jumps

In order to characterizc large fluctuations of the financial markets and optimize financial portfolio, a new dynamic asset control strategy was proposed in this work. Firstly, a random process item with variable jump intensity was introduced to the existing discrete microstructure model to denote large price fluctuations. The nonparametric method of LEE was used for detecting jumps. Further, the extended Kalman filter and the maximum likelihood method were applied to discrete microstructure modeling and the estimation of two market potential variables： market excess demand and liquidity. At last, based on the estimated variables, an assets allocation strategy using evolutionary algorithm was designed to control the weight of each asset dynamically. Case studies on IBM Stock show that jumps with variable intensity are detected successfully, and the assets allocation strategy may effectively keep the total assets growth or prevent assets loss at the stochastic financial market.

Bayesian Segmentation of Piecewise Linear Regression Models Using Reversible Jump MCMC Algorithm

Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation ofpiecewise linear regression models. The method used to estimate the parameters ofpicewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC （Marcov Chain Monte Carlo） algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters ofpicewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps

A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.

Structural jump-diffusion model for pricing collateralized debt obligations tranches

This paper considers the pricing problem of collateralized debt obligations tranches under a structural jump-diffusion model, where the asset value of each reference entity is generated by a geometric Brownian motion and jump with an asymmetric double exponential distribution. Conditioned on the common factor of individual entity, this paper gets the conditional distribution, and further obtains the loss distribution of the whole reference portfolio. Based on the semi-analytic approach, the fair spreads of collateralized debt obligations tranches, i.e., the prices of collateralized debt obligations tranches, are derived.