Continuous-time Model Research Articles

Predictable forward performance processes in complete markets

We establish existence of Predictable Forward Performance Processes (PFPPs) in conditionally complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the investment horizon can be finite or infinite. We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation, which is the counterpart of the functional equation found in the binomial case. Although this integral equation has been partially studied in the existing literature, we provide a new solution method using the Fourier transform for tempered distributions. We also provide closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class. We apply our results to two special cases. The first one is the binomial market and is included to relate our work to the existing literature. The second example considers a generalized Black–Scholes model which, to the best of our knowledge, is a new result.

Comparison of dynamic behavior between continuous- and discrete-time models of intraguild predation.

Intraguild predation is a common ecological phenomenon that manifests itself by the aggression of one predator by another to obtain a shared prey species. In this paper, we develop a discrete analog of a stoichiometric continuous-time intraguild predation model. We analyze the dynamics of the discrete-time model, such as boundedness and invariance, stability of equilibria, and features of ecological matrices. The dynamic behavior of the two models is compared and analyzed through numerical analysis. We observe the same coexistence region of populations and stoichiometric effects of food quality of the shared prey in both models. Obvious differences between the discrete- and continuous-time models can be observed with intermediate and high levels of light intensity. The multistability characteristics and the existence interval of chaos differ among the different time scale models. This study provides evidence of the importance of time scales on intraguild predation.

Continuous-Time Modeling and Analysis of Particle Beam Metrology

Particle beam microscopy (PBM) performs nanoscale imaging by pixelwise capture of scalar values representing noisy measurements of the response from secondary electrons (SEs) integrated over a dwell time. Extended to metrology, goals include estimating SE yield at each pixel and detecting differences in SE yield across pixels; obstacles include shot noise in the particle source as well as lack of knowledge of and variability in the instrument response to single SEs. A recently introduced time-resolved measurement paradigm promises mitigation of source shot noise, but its analysis and development have been largely limited to estimation problems under an idealization in which SE bursts are directly and perfectly counted. Here, analyses are extended to error exponents in feature detection problems and to degraded measurements that are representative of actual instrument behavior for estimation problems. For estimation from idealized SE counts, insights on existing estimators and a superior estimator are also provided. For estimation in a realistic PBM imaging scenario, extensions to the idealized model are introduced, methods for model parameter extraction are discussed, and large improvements from time-resolved data are presented.

Chaos Elimination for a Buck Converter Using the Multi-Objective Grey Wolf Optimiser

Abstract A wide variety of nonlinear phenomena, such as bifurcation and chaos, have been observed in power electronics converters. Much research has been conducted on these behaviours in different converter topologies. The buck converter is known to exhibit chaotic behaviour in a wide parameter range, giving rise to unstable behaviours depending on the circuit parameters values. This paper investigates this bifurcation behaviour by varying the parameters of a voltage PI (Proportional Integral) controlled buck converter operating in continuous conduction mode, using a continuous-time model and constant frequency control signal. Furthermore, a novel and improved version of the PI compensation technique, designed using the multi-objective grey wolf optimiser (MOGWO), is proposed to stabilise the buck converter from chaotic state to periodic orbit.

Risk-seeking insider trading with partial observation in continuous time

<abstract><p>In this paper, a continuous-time insider trading model is investigated in which an insider is risk-seeking and market makers may receive partial information on the value of a risky asset. With the help of filtering theory and dynamic programming principle, the uniqueness and existence of linear equilibrium is established. It shows that (ⅰ) as time goes by, the residual information decreases, but both the trading intensity and the market liquidity increases, and (ⅱ) with the partial observation accuracy decreasing, both the market liquidity and the residual information will increase while the trading intensity decreases. On the whole, the risk-seeking insider is eager to trade all the trading period, and for market development, it is necessary to increase the insider's risk-preference behavior appropriately.</p></abstract>

Probability of disease extinction and outbreak in a stochastic tuberculosis model with fast-slow progression and relapse

<abstract><p>A stochastic continuous-time Markov chain tuberculosis model with fast-slow progression and relapse is established to explore the impact of the demographic variation on TB transmission. At first, the extinction threshold and probability of the disease extinction and outbreak are obtained by applying the multitype Galton-Waston branching process for the stochastic model. In numerical simulations, the probability of the disease extinction and outbreak and expected epidemic duration of the disease are estimated. To see how demographic stochasticity affects TB dynamics, we compare dynamical behaviors of both stochastic and deterministic models, and these results show that the disease extinction in stochastic model would occur while the disease is persistent for the deterministic model. Our results suggest that minimizing the contact between the infectious and the susceptible, and detecting the latently infected as early as possible, etc., could effectively prevent the spread of tuberculosis.</p></abstract>

Double-quantized-based $ H_{\infty} $ tracking control of T-S fuzzy semi-Markovian jump systems with adaptive event-triggered

<abstract><p>This paper investigates the issue of asynchronous $ H_{\infty} $ tracking control for nonlinear semi-Markovian jump systems (SMJSs) based on the T-S fuzzy model. Firstly, in order to improve the performance of network control systems (NCSs) and the efficiency of data transmission, this paper adopts a double quantization strategy which quantifies the input and output of the controllers. Secondly, for the purpose of reducing the burden of network communication, an adaptive event-triggered mechanism (AETM) is adopted. Thirdly, due to the influence of network-induce delay, the system mode information can not be transmitted to the controller synchronously, thus, a continuous-time hidden Markov model (HMM) is established to describe the asynchronous phenomenon between the system and the controller. Additionally, with the help of some improved Lyapunov-Krasovski (L-K) functions with fuzzy basis, some sufficient criteria are derived to co-guarantee the state stability and the $ H_{\infty} $ performance for the closed-loop tracking control system. Finally, a numerical example and a practical example are given to verify the effectiveness of designed mentality.</p></abstract>

Global terrestrial temperature modeling by using fractional models

Modeling the global climate system through the temperature output is a very challenging task. Knowing the fractional operator long memory property to well model diffusion phenomena with very few parameters, it is proposed in this paper to use fractional models for climate change modeling. System identification is applied for continuous-time system identification of multiple-input single-output (MISO) fractional order models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. Finally, the estimation with fractional models is carried out on real input/output data and provide a very good goodness fit of the global earth temperature.

DYNAMIC ANALYSIS OF A DISCRETE AMENSALISM MODEL WITH ALLEE EFFECT

This paper concerns with a discretization of a continuous-time amensalism model with Allee effect on the first species. Compared with the continuous analog, the discrete system has different and much richer dynamical behaviors. First, we obtain the existence of fixed points and their local stability. Then we confirm the occurrence of fold bifurcation and period doubling bifurcation by using the center manifold theorem and bifurcation theory. Followed is a hybrid control strategy to control the period-doubling bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulations indicate that Allee effect is beneficial to the stability of the first species to a certain extent. Moreover, when the first species is affected by Allee effect, solutions can approach the corresponding fixed point more quickly.

Stability Analysis of a Socially Inspired Adaptive Voter Model

In this letter, we study an instance of continuous-time voter model over directed graphs on social networks with a specific refinement: the agents can break or create new links in the graph. The edges of the graph thus <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">co-evolve</i> with the agents’ spin. Specifically, the agents may break their links with neighbours of different spin, and create links their 2-hop neighbours, provided they have same spin. We characterize the absorbing configurations and present a particular case that corresponds to a single agent facing two antagonistic ideologies. By asymptotic analysis, we observe two regimes depending on the parameters: in one regime, hesitation disappears rapidly, while when the link creation rate is high enough, slow extinction occurs. We compute the threshold value and illustrate these results with numerical simulations.

Stability Analysis of Logit Dynamics with Committed Minority and Internal/External Conformity Biases

In this paper, we analyze a novel continuous-time dynamical binary choice model that unifies several logit dynamics in the presence of a committed minority and internal/external conformity biases. Each logit dynamics represents a population of decision makers in a group (i.e., a subset of society), who choose one from two available strategies. The internal conformity bias is regarded as an inertia which causes people in the group to stick with their own majority. The external conformity bias indicates a social coordination which drives every person in society to the social majority. Based on control theoretic insights, we prove that the committed minority eventually supersedes the majority when every person has an appropriately bounded rationality. Numerical experiments demonstrate the present analytical results.

Design of Switching-type Dynamic Quantizers for Continuous-Time Nonlinear Systems

This paper focuses on designing discrete-valued input systems using dynamic quantizers, which convert continuous-valued signals into discrete ones. Although the optimal design of dynamic quantizer is much studied, there are some unresolved problems. This study focuses on one of the unresolved problems: the design of a switching-type discrete-time dynamic quantizer for continuous-time nonlinear systems. In this paper, we first reduced the quantizer design problem to a selection problem of continuous-time linear models for a given nonlinear system. Then, we evaluated this approach via simulations of the swing-up problem for a cart-type inverted pendulum.

Insider trading with dynamic asset under market makers' partial observations

&lt;abstract&gt;&lt;p&gt;This paper studies an extended continuous-time insider trading model of Calentey and Stacchetti (2010, Econometrica), which allows market makers to observe some partial information about a dynamic risky asset. For each of the two cases with trading until either a fixed time or a random time, we establish the existence and uniqueness of linear Bayesian equilibrium, consisting of insider trading intensity, price pressure on market orders and price pressure on asset observations. It shows that at each of the two equilibria, all information on the risky asset is incorporated in the market price and when the volatility of observation noise keeps constant, the more information observed by market makers, the smaller price pressure on market orders but the greater price pressure on asset observations such that the insider earns less profit and vice versa. It suggests that the partial observation of market makers weakens the information advantage of the insider, which prevents the insider from monopolizing the market to make excessive profit, then reduces the losses of noise traders, thus improving the fairness and effectiveness in the insider trading market.&lt;/p&gt;&lt;/abstract&gt;

Discrete Geometric Control of Planar Flexible Link Manipulators

Discrete control laws for flexible beam models obtained using structure-preserving discretization procedures are few in the existing literature so far and many control laws, including distributed ones, exist for continuous time models. Much of the effort has focussed on the discretization of the flexible structure and the fidelity of such models. The work in this paper examines the feasibility of a discretized version of a continuous time distributed control strategy, with a few approximations, to the discrete variational integrator of a flexible beam, in our case, a flexible single-link manipulator (FLM). The nonlinear control strategy is inspired by a potential shaping method in the literature based on the Cosserat continuum framework. We provide stability proof for this continuous-time control and approximate it to a discrete-time geometric framework. We use a geometrically exact beam model in which the manipulator's configuration space lies on an infinite-dimensional Lie group. The model-based discrete-time control uses a Lie Group Variational Integrator obtained by applying the variational principle on the Lagrangian of the FLM. Results show that the discrete closed-loop system stabilizes the FLM at setpoints during point-to-point rotational maneuvers. The controller demands fine time-sampling and we acknowledge the associated challenges for real-time implementation of the control scheme and intend to pursue it as our future work.

Flatness Analysis for the Sampled-data Model of a Single Mast Stacker Crane

We show that the Euler-discretization of the nonlinear continuous-time model of a single mast stacker crane is flat. The construction of the flat output is based on a transformation of a subsystem into the linear time-variant discrete-time controller canonical form. Based on the derived flat output, which is also a function of backward-shifts of the system variables, we discuss the planning of trajectories to achieve a transition between two rest positions and compute the corresponding discrete-time feedforward control.

Continuous-time modeling of financial returns based on Limit Order Book data

The Limit Order Book (LOB) of a financial security contains the list of buy and sell orders placed by traders on a single or across many exchanges for a given stock. As such, the amount of information contained in the LOB is much richer than that contained in the time history of the mean price, so it can potentially be exploited to model and predict more accurately the future returns. As far as we are aware, this work offers - for the first time - a dynamical systems perspective on the latter modeling problem, leading to a two-fold contribution: (i) we will define a new regressor, called Base Imbalance, and we will show that its predictive potential is more significant than the ones usually employed in the literature; (ii) we will discuss that the most suitable way to derive a model of the LOB dynamics is via continuous-time system identification, due to the event-based nature of the phenomenon at hand. The effectiveness of the proposed modeling strategy to be used in trading policies will be illustrated by means of a benchmark experimental data.

Continuous-Time Model Identification of the Subglottal System

Continuous-Time Model Identification of the Subglottal System

A jumping index of jumping stocks? An MCMC analysis of continuous-time models for individual stocks

A jumping index of jumping stocks? An MCMC analysis of continuous-time models for individual stocks

Indirect Data-Driven Observer Design Using Neural Canonical Observer Structures

An indirect data-driven observer design approach for nonlinear discrete-time systems based on an input-output injection with neural canonical observer structures is proposed. An artificial neural network auto-encoder structure, trained with recorded state, input, and output data, is used for the identification of a system in a nonlinear Brunovsky observer form with output transformation. The neural approximations of the transformations and the input-output injection can be used to construct an observer with linear error dynamics using methods from linear control theory. The approach is demonstrated on two academic examples and on an industrially-motivated problem with a sampled continuous-time model.

Optimal product release time for a new high-tech startup firm under technical uncertainty

&lt;p style='text-indent:20px;'&gt;Decision makers of new high-tech startup firms always want to choose an optimal time to launch their products which are under research and development (R&amp;amp;D) to obtain the maximum net income of these firms. However, existing models fail to consider the optimal release time of products for these new high-tech startup firms. In this paper, the optimal time to launch the product of the R&amp;amp;D project is assumed to be the first time when the product of the R&amp;amp;D project is released to the market. Based on this assumption, we develop a continuous-time model to find the optimal time at which the startup firm launches its product of the R&amp;amp;D project by considering the price of the similar product. Employing the methods of dynamic programming and variational inequalities, we also provide a closed form solution to our model. We also find that these high-tech startup firms prefer to delay their product release time when the price of the similar product is at a phase of rapid growth or the price has considerable uncertainty. Moreover, some numerical examples are provided to investigate the properties of our model.&lt;/p&gt;