이산시간 이자율기간구조모형

박정민 ( Jeong Min Park ),조재호 ( Jae Ho Cho ) 한국금융연구원 2012 금융연구 Vol.26 No.3

The term structure theory of interest rates has long been an important subject in economics and finance as it is widely used for diverse purposes such as valuing bonds and interest rate derivative securities, managing bond portfolios, and making monetary policies. Since Vasicek (1977) and Cox, Ingersoll, and Ross (1985), numerous studies have introduced dynamic term structure models (DTSMs) in various settings. DTSMs developed so far may be classified into continuous vs discrete time models on the one hand, and equilibrium vs arbitrage models on the other. This paper aims at a review of existing equilibrium DTSMs in discrete time in order to discuss some recent issues and to shed light on the direction of future research in this area. Although, since Vasicek (1977) and Cox, Ingersoll, and Ross (1985), continuous time models seem to have been more popular in both theoretical and empirical studies, a variety of discrete time models have also been developed. While continuous time models may be advantageous for obtaining closed-form solutions of bond prices, discrete time models can be more useful for empirical analyses to reflect the fact that bond prices (or interest rates) in reality are observed at discrete time intervals. The difficulty in estimating continuous time models for practical purposes arises from the facts, in particular, that it is necessary to discretize continuous time stochastic processes of latent state variables, and that it may not be possible to obtain analytical transition probability density functions of the discretized stochastic processes. In this paper, we classify discrete time DTSMs into two categories: one is the ``continuous-time model analog`` in which continuous time stochastic processes are Euler-discretized, and the other is the ``exact discrete-time model`` in which state variables follow discrete time exponential affine processes, of which the Car (compound autoregressive) process is typical. The continuous time model analogs result from approximations of stochastic processes of latent state variables via a simple discretization at the same frequency with other observable variables available. While these discretized processes might appear to have the same form as the corresponding continuous time processes, they do not preserve all the properties of their counterparts. For instance, state variables in discretized processes can be negative even if the Feller condition, which guarantees the non-negativity of continuous time state variables, is met. Moreover, the non-negativity may be obtained in discretized processes although the Feller condition is violated. Also, it may not be possible to obtain the closed-form transition probability density functions of state variables. The exact discrete time models are specified and characterized by a special class of discrete time exponential affine processes called Car processes. These processes fulfill the properties of their continuous time counterparts and make it possible to obtain closed-form transition probability density functions. Thus, the exact discrete time models resolve the problems of the continuous time model analogs. We discuss characteristics and limitations of respective models in each category by comparing with those of their continuous-time counterparts in this vein. The paper is organized as follows. Section 2 reviews some basic knowledge on the dynamic term structure theory of interest rates. Section 3 introduces continuous time model analogs, dividing them into uni-variate vs multivariate models and linear vs nonlinear models. Section 4 introduces the properties and representatives of Car processes that constitute exact discrete-time models. Also, this section surveys related studies put forth recently and compares them with continuous time model analogs. Finally, section 5 summarizes and concludes.

Uniform-in-time transition from discrete dynamics to continuous dynamics in the Cucker-Smale flocking

Ha, Seung-Yeal,Zhang, Xiongtao World Scientific Publishing Company 2018 MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES Vol.28 No.9

<P>We study a <I>uniform-in-time convergence</I> from the discrete-time (in short, discrete) Cucker-Smale (CS) model to the continuous-time CS model, which is valid for the <I>whole time interval</I>, as time-step tends to zero. Classical theory yields the convergence results which are valid only in <I>any finite-time interval</I>. Our uniform convergence estimate relies on two quantitative estimates “<I>asymptotic flocking estimate</I>” and “<I>uniform</I><TEX>$ \ell _{2}$</TEX><I>-stability estimate with respect to initial data</I>”. In the previous literature, most studies on the CS flocking have been devoted to the continuous-time model with general communication weights, whereas flocking estimates have been done for the discrete-time model with special network topologies such as the complete network with algebraically decaying communication weights and rooted leaderships. For the discrete CS model with a regular and algebraically decaying communication weight, asymptotic flocking estimate has been extensively studied in the previous literature. In contrast, for a general decaying communication weight, corresponding flocking dynamics has not been addressed in the literature due to the difficulty of extending the Lyapunov functional approach to the discrete model. In this paper, we present asymptotic flocking estimate for the discrete model using the Lyapunov functional approach. Moreover, we present a uniform <TEX>$ \ell _{2}$</TEX>-stability estimate of the solution for the discrete CS model with respect to initial data. We combine asymptotic flocking estimate and uniform stability to derive a uniform-in-time convergence from the discrete CS model to the continuous CS model, as time-step tends to zero.</P>

Numerical Exact Discrete-Time-Model of Linear Time-Varying Systems

Hiroaki Shiobara,Noriyuki Hori 제어로봇시스템학회 2008 제어로봇시스템학회 국제학술대회 논문집 Vol.2008 No.10

This paper proposes a method of obtaining a numerical, exact discrete-time-model for linear time-varying systems. The method relies on the computation of a transition matrix expressible as the Peano-Baker Series for a given discrete-time interval and system parameters. For time-invariant systems, the proposed discrete-time model reduces to the well known step-invariant-model. As an example, the Euler differential equation is discretized using the standard forward-difference method, the discretization of Euler differential operator, and the proposed method. Simulations show that the proposed discrete-time-model gives exact values at discrete-time instants for any discretization periods, while the other two methods generate errors.

이산시간을 가지는 직장암 4기 자료의 분석에 관한 연구

이민정(Minjung Lee) 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.1

생존자료를 분석하기 위한 대부분의 통계적 모형과 방법론들은 연속형 생존시간이 관측되었다는 가정을 바탕으로 개발되어 왔다. 그러나 이산시간이 관측될 수도 있다. 그런 경우, 이산시간모형을 이용하여 생존자료를 분석하는 것이 적절하다. 본 논문에서는 이산시간을 가지는 생존자료에 대하여 회귀분석하는 방법에 관하여 연구하였다. 이산시간모형의 모수를 추정하기 위하여 우도함수를 이용하였고, 이를 바탕으로 생존함수를 추정하였다. 미국 국립암연구소의 SEER 프로그램에서 제공하는 직장암 4기 자료에 이산시간모형을 적합하여 직장암 4기 환자의 생존율을 추정하였다. 적합된 모형의 타당성을 검증하기 위하여 calibration 도표와 시간에 의존하는 ROC 곡선 아래 면적을 계산하였으며, 이를 통해 적합된 모형의 타당성을 확인하였다. In the analysis of survival data, most analysis methods have been developed based on continuous time data. However, discrete event times may be observed. It would be appropriate to use a discrete time model for analyses of such data. In this paper, we studied regression analyses of discrete time survival data. We used maximum likelihood inferences for estimation of the parameters in a discrete hazards model and presented prediction for the discrete survival function. We fitted the discrete time proportional odds model to state IV rectal cancer data obtained from the Surveillance, Epidemiology, and End Results program of the National Cancer Institute and estimated the survival probability for a patient with specific covariate values under the discrete time proportional odds model. We evaluated calibration and discriminatory accuracy of the fitted model using calibration plot and time-dependent area under the ROC curve. Through these results, we confirmed the validity of the fitted model.

Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: Exact discrete-time design approach

Kim, D.W.,Lee, H.J. North-Holland 2012 Fuzzy Sets and Systems Vol. No.

This paper presents a new direct discrete-time design methodology of a sampled-data observer-based output-feedback fuzzy controller for a class of nonlinear system that is exactly modeled in Takagi-Sugeno's form at least locally. A fundamental yet challenging issue in this direction is the unavailability of the exact discrete-time model of the nonlinear plant in a closed form. In contrast to the earlier works that are based on an approximate discrete-time model thus the stability obtained in the design step is not preserved in the implementation step, we employ an exact discrete-time fuzzy model in an integral form. Sufficient asymptotic stabilization conditions are investigated in the discrete-time Lyapunov sense. We then show that the resulting sampled-data controller indeed asymptotically stabilizes the nonlinear plant. An example is provided to illustrate the effectiveness of the proposed methodology.

평균전류모드제어의 전류응답예측을 위한 새로운 이산시간 소신호 모델

정영석 전력전자학회 2005 전력전자학회 논문지 Vol.10 No.3

In this paper, a new discrete-time small signal model of an average current mode control is proposed to predict the inductor current responses. Compared to the peak current mode control, the analysis of the average current mode control is difficult because of its presence of an compensation network. By utilizing sampler model, a new discrete-time small signal model is derived and used to predict the behaviors of an inductor current of average current mode control employing generalized compensation networks. In order to show the usefulness of the proposed model, prediction results of the proposed model are compared to those of the circuit level simulator, PSIM and experiment. 본 논문에서는 평균전류모드제어를 이용하는 컨버터의 전류응답을 예측할 수 있는 새로운 이산시간 소신호 모델을 구한다. 평균전류모드제어는 최대전류모드제어와 달리 전류제어를 위해 복잡한 보상기 회로를 사용하므로 컨버터의 동작 특성 해석이 어렵다. 평균전류모드제어를 사용하는 컨버터의 소신호 전류응답을 예측하기 위해 샘플러 모델을 제안하고, 이 모델로부터 새로운 이산시간 소신호 모델을 구한다. 제안된 방식은 기존 방식과 달리 복잡한 형태의 보상기를 사용하는 컨버터에도 적용 가능하다. 제안한 새로운 이산시간 소신호 모델을 이용한 예측 결과를 스위칭 모델 시뮬레이션 프로그램인 PSIM을 이용한 시뮬레이션 결과 및 실험결과와 비교하여 제안한 새로운 이산시간 소신호 모델의 우수성을 보인다.

리튬 이온 전지의 전기적 등가 회로에 관한 연속시간 및 이산시간 상태방정식 연구

한승윤,박진형,박성윤,김승우,이평연,김종훈 전력전자학회 2020 전력전자학회 논문지 Vol.25 No.4

Estimating the accurate internal state of lithium ion batteries to increase their safety and efficiency is crucial. Various algorithms are used to estimate the internal state of a lithium ion battery, such as the extended Kalman filter and sliding mode observer. A state-space model is essential in using algorithms to estimate the internal state of a battery. Two principal methods are used to express the state-space model, namely, continuous time and discrete time. In this work, the extended Kalman filter is employed to estimate the internal state of a battery. Moreover, this work presents and analyzes the estimation performance of algorithms consisting of a continuous time state-space model and a discrete time state-space model through static and dynamic profiles.

의사결정 단계와 시간지연을 고려한 이산시간 전투 모형 연구

윤봉규 한국국방경영분석학회 2023 한국국방경영분석학회지 Vol.49 No.2

Recently, there has been a growing interest in combat models due to the increasing need for the development of tactics in 'algorithmic warfare', particularly with the rise in the utilization of autonomous weapons on the battlefield including drones. Two primary approaches have emerged for the development of combat models: equation-based analytic models and simulation-based models. While both approaches possess their own strengths, simulation methods have gained popularity due to their ease of use. Moreover, NetLogo, a dis- crete-time simulation language, has become increasingly prevalent in various applications, owing to its low barrier to entry and its ability to simulate real-world phenomena. Nevertheless, NetLogo models are limited by their reliance on discrete-time simulation languages, thereby hindering their utilization of numerous analytic results based on continuous-time methodologies. Moreover, the challenge lies in the complexity of customizing a model to various scenarios. This paper presents two discrete-time combat models employing both equation-based analytic approach and simulation approach. The equation-based analytic model utilizes Phase-type distribution to describe the decision stages of combatants, while the simulation model is constructed using NetLogo. By con- ducting a comparative analysis of these two models for verification purposes, this paper aims to provide a vali- dated discrete-time combat model that exhibits strong adaptability to various battlefield situations.

Methodology Proposal to Estimate Korean ICT Start-ups’ Survival: A Discrete-time Proportional Hazard Model

( Kyunghoon Kim ) 정보통신정책학회 2019 정보통신정책연구 Vol.26 No.3

This study is concerned with factors affecting start-ups’ survival, and with predicting their survival probability. A new proportional hazard model is proposed for analyzing the survival of information and communications technology (ICT) start-ups. This model overcomes the limitations of existing survival models in their utilization of information about firms’ activities, stemming from the fact that those models manipulate observations only in a continuous-time horizon. A discrete-time proportional hazard model is proposed to account exhaustively for firms’ activities within the study period. To show the superiority of the proposed discrete-time proportional hazard model over a benchmark continuous-time proportional hazard model, both models are applied to a clinical dataset and their log-likelihood values are compared. The proposed model is found to be better in terms of goodness-of-fit and predictive performance.

Methodology Proposal to Estimate Korean ICT Start-ups’ Survival: A Discrete-time Proportional Hazard Model

김경훈 정보통신정책학회 2019 정보통신정책연구 Vol.26 No.3

This study is concerned with factors affecting start-ups’ survival, and with predicting their survival probability. A new proportional hazard model is proposed for analyzing the survival of information and communications technology (ICT) start-ups. This model overcomes the limitations of existing survival models in their utilization of information about firms’ activities, stemming from the fact that those models manipulate observations only in a continuous-time horizon. A discrete-time proportional hazard model is proposed to account exhaustively for firms’ activities within the study period. To show the superiority of the proposed discrete-time proportional hazard model over a benchmark continuous-time proportional hazard model, both models are applied to a clinical dataset and their log-likelihood values are compared. The proposed model is found to be better in terms of goodness-of-fit and predictive performance.