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The purpose of this paper is to demonstrate new properties of continuous‐ and discrete‐time dynamical systems.

First, definitions of two types of spatial symmetry are introduced. These are used as definitions, which, along with existing knowledge show that it is possible to identify properties of dynamical systems that were previously unknown.

The main result of the paper is a new theorem regarding new properties of continuous‐ and discrete‐time dynamical systems.

The present study provides a starting point for further research on the differences between continuous‐ and discrete‐time dynamical systems. This work builds on the definition of spatial symmetry.

The theorem proved in this paper and the new properties of dynamical systems can be used to introduce new methods of approximating continuous‐time dynamical systems by discrete‐time dynamical systems and vice versa. Such approaches can also be helpful in constructing chaotic sources to model noise.

This paper offers contributions to the broader discussion of differences between continuous‐ and discrete‐time dynamical systems. In particular, the paper supports the statement that many discrete‐time processes cannot be embedded into continuous ones.

This paper aims to develop a methodology to accurately and timely measure movements in housing markets by constructing a continuously estimated house price index.

The continuous index, which is extracted from an additive model that includes the temporal and the locational effects as smooth functions, can be interpreted as an extension of the classical hedonic time-dummy method. The methodology is applied to housing sales from Sydney, Australia, between 2001 and 2011, and compared to three types of discrete indexes.

Discrete indexes turn out to approach the continuously estimated index with decreasing period lengths but eventually become wiggly and unreliable because of fewer observations per period. The continuous index, in contrast, is stable, has favourable robustness properties and is more objective in several ways.

The resulting index tracks movements in the housing market precisely and in “real-time” and is hence suited for monitoring and assessing housing markets. Because turbulence in housing markets is often a harbinger of financial crises, such monitoring tools support policymakers and investors in tailoring their decisions and reactions. Additionally, the index can be evaluated arbitrarily frequently and therefore is well suited for use in property derivatives.

The purpose of this paper is to improve the transient response and the inter‐sample behavior of a model reference adaptive control system by an appropriate selection of the fractional order hold (FROH) gain β and the multirate gains used in the control reconstruction signal through a fully freely chosen reference model even when the continuous plant possesses unstable zeros.

A multiestimation adaptive control scheme for linear time‐invariant continuous‐time plant with unknown parameters is presented. The set of discrete adaptive models is calculated from a different combination of the correcting gain β in a FROH and the set of gains to reconstruct the plant input under multirate sampling with fast input sampling. Then the scheme selects online the model with the best continuous‐time tracking performance which includes a measure of the inter‐sample ripple, which is improved. The estimated discrete unstable zeros are avoided through an appropriate design of the multirate gains so that the reference model might be freely chosen with no constraints on potential unstable zeros.

The scheme is able to select online the discretization model with the best continuous‐time tracking performance without an appropriate initialization.

The switching mechanism among the different models should maintain in operation the active discretization model at least for a minimum residence time in order to guarantee closed‐loop stability. The inter‐sample behavior is improved, but it is not always completely removed.

The transient response and the inter‐sample behavior are improved by using this multiestimation‐based discrete controller compared with a single estimation‐based one. The implementation of discrete controllers makes it easier and cheaper to implement and also more reliable than continuous‐time controllers.

The main innovation of the paper compared with previous background work is that the reference output is supplied by a stable continuous transfer function. Then the scheme is able to partly regulate the continuous‐time tracking error while the controller is essentially discrete‐time and operated by a FROH in general.

To provide an overview of how a number of frequently used smoothing‐based forecasting techniques can be modelled for use in dynamic analysis of production‐inventory systems.

The smoothing techniques are modelled using transfer functions and state space representation. Basic control theory is used for analysing the dynamic properties.

A set of expressions are derived for the smoothing techniques and dynamic properties are identified.

Dynamic properties are important in many applications. It is shown that the different smoothing techniques can have very different influences on the dynamic behaviour and therefore should be considered as a factor when smoothing parameters are decided on.

Dynamic behaviour of production‐inventory systems can be analysed using control theory based on, e.g. transfer functions or state space models. In this paper a set of models for five common smoothing techniques are analysed and their respective dynamic properties are highlighted.

The purpose of this paper is to consider a discrete‐time, Markov, regime‐switching, affine term‐structure model for valuing bonds and other interest rate securities. The proposed model incorporates the impact of structural changes in (macro)‐economic conditions on interest‐rate dynamics. The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The market in the proposed model is, in general, incomplete. A modified version of the Esscher transform, namely, a double Esscher transform, is used to specify a price kernel so that both market and economic risks are taken into account.

The authors derive a simple way to give exponential affine forms of bond prices using backward induction. The authors also consider a continuous‐time extension of the model and derive exponential affine forms of bond prices using the concept of stochastic flows.

The methods and results presented in the paper are new.

The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company.

Starting with a basic solvency model, the authors study the impact of the discretization interval on risk measures. The analysis considers the sensitivity of the discrepancy between the risk measures in continuous and discrete time to various parameters, such as the asset-to-liability ratio, the characteristics of the asset and liability processes, as well as the correlation between assets and liabilities. Capital requirements for the one-year planning horizon in continuous vs discrete time are reported as well. The purpose is to report the degree to which the deviations in risk measures, due to the different discretization intervals, can be reduced by means of increasing the frequency with which the risk measures are assessed.

The simulation results suggest that the risk measures of an insurance company are consistently underestimated when assessed on an annual basis (as it is currently done under insurance regulation such as Solvency II). The authors complement the analysis with the capital requirements of an insurance company and conclude that more frequent discretization translates into higher capital requirements for the insurance company. Both the probability of ruin and the expected policyholder deficit (EPD) can be reduced through intermediate financial reports.

The results from our simulation analysis suggest that that the choice of discretization interval has an impact on the risk assessment of an insurance company which uses the probability of ruin and the EPD as risk measures. By assessing the risk measures once a year, both risk measures and the capital requirements are consistently underestimated. Therefore, the recommendation for risk managers is to complement the capital requirements in solvency regulation with sensitivity analyses of the risk measures presented with respect to time discretization. On the one hand, it seems to us that there is value in knowing about the substantial discrepancy between the focused time discrete ruin probability and EPD compared to the continuous version. On the other hand, and if there are no substantial transaction costs associated with more frequent monitoring of solvency figures, a frequent update would be helpful to increase the accuracy of the calculations and reduce the EPD.

The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

This study/paper aims to present a separable identification algorithm for a multiple input single output (MISO) continuous time (CT) hybrid “Box–Jenkins”.

This paper proposes an optimal method for the identification of MISO CT hybrid “Box–Jenkins” systems with unknown time delays by using the two-stage recursive least-square (TS-RLS) identification algorithm.

The effectiveness of the proposed scheme is shown with application to a simulation example.

A two-stage recursive least-square identification method is developed for multiple input single output continuous time hybrid “Box–Jenkins” system with multiple unknown time delays from sampled data. The proposed technique allows the division of the global CT hybrid “Box–Jenkins” system into two fictitious subsystems: the first one contains the parameters of the system model, including the multiple unknown time delays, and the second contains the parameters of the noise model. Then the TS-RLS identification algorithm can be applied easily to estimate all the parameters of the studied system.

In this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.

The authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).

The optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.

In conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).

The results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.

First, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.

The pressure is on organizations to go beyond automating their internal audit activities and develop and integrate internal auditing into business processes of the enterprise. This paper aims to propose a “full power” continuous auditing (CA) model with three key components: electronic audit evidence functions; intra‐process auditing; and inter‐process auditing.

This paper follows a design science approach by identifying relevant problems from the current literature, defining the objectives of the study, designing and developing the “full power” CA model, and evaluating the model. The model supports business process‐centric auditing and enhances the business monitoring capacities of organizations enabling the fulfillment of increasingly stringent compliance requirements with internal policies as well as external regulations.

This work has attempted to fill the gap between the enterprise solutions offered by enterprise system providers and a structured approach to auditing within enterprise environments by proposing the IIPCA model which combines the automated controls inherent in the systems with continuous audits based on electronic audit evidence. The approach provides for auditing both within and between processes ensuring comprehensiveness of the audit process.

The paper makes a contribution by proposing a “full power” continuous auditing model on the principle of continuous monitoring and with predefined building block components; facilitating the integration of continuous auditing within business information processing in an enterprise using different building blocks; and giving practitioners insight on the adoption of the CA in the enterprise and how it will enhance their audit effectiveness, and audit efficiency.