scholarly journals Optimal measurement budget allocation for Kalman prediction over a finite time horizon by genetic algorithms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Aspeel ◽  
Axel Legay ◽  
Raphaël M. Jungers ◽  
Benoit Macq
Keyword(s):  
Genetic Algorithm ◽  
Discrete Time ◽  
Continuous Time ◽  
Estimation Error ◽  
Budget Allocation ◽  
Finite Horizon ◽  
Time Step ◽  
Optimal Measurement ◽  
Discrete Time Dynamical System ◽  
The Impact

AbstractIn this paper, we address the problem of optimal measurement budget allocation to estimate the state of a linear discrete-time dynamical system over a finite horizon. More precisely, our aim is to select the measurement times in order to minimize the variance of the estimation error over a finite horizon. In addition, we investigate the closely related problem of finding a trade-off between number of measurements and signal to noise ratio.First, the optimal measurement budget allocation problem is reduced to a deterministic combinatorial program. Then, we propose a genetic algorithm implementing a count preserving crossover to solve it. On the theoretical side, we provide a one-dimensional analysis that indicates that the benefit of using irregular measurements grows when the system is unstable or when the process noise becomes important. Then, using the duality between estimation and control, we show that the problem of selecting optimal control times for a linear quadratic regulator can be reduced to our initial problem.Finally, numerical implementations demonstrate that using measurement times optimized by our genetic algorithm gives better estimate than regularly spaced measurements. Our method is applied to a discrete version of a continuous-time system and the impact of the discretization time step is studied. It reveals good convergence properties, showing that our method is well suited to both continuous-time and discrete-time setups.

Hedging in discrete time under transaction costs and continuous-time limit

1999 ◽  
Vol 36 (1) ◽  
pp. 163-178 ◽  
Author(s):  
Pierre-F. Koehl ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Risky Asset ◽  
Market Model ◽  
Upper And Lower Bounds ◽  
Time Step ◽  
Proportional Transaction Costs ◽  
Call Options

We consider a discrete-time financial market model with L1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

A FINITE-HORIZON OPTIMAL INVESTMENT AND CONSUMPTION PROBLEM USING REGIME-SWITCHING MODELS

2014 ◽  
Vol 17 (04) ◽  
pp. 1450027 ◽  
Author(s):  
R. H. LIU
Keyword(s):  
Continuous Time ◽  
Regime Switching ◽  
Optimal Investment ◽  
Finite Horizon ◽  
Power Utility ◽  
Verification Theorem ◽  
Regime Switching Models ◽  
Switching Models ◽  
The Impact ◽  
Optimal Investment And Consumption

This paper is concerned with a finite-horizon optimal investment and consumption problem in continuous-time regime-switching models. The market consists of one bond and n ≥ 1 correlated stocks. An investor distributes his/her wealth among these assets and consumes at a non-negative rate. The market parameters (the interest rate, the appreciation rates and the volatilities of the stocks) and the utility functions are assumed to depend on a continuous-time Markov chain with a finite number of states. The objective is to maximize the expected discounted total utility of consumption and the expected discounted utility from terminal wealth. We solve the optimization problem by applying the stochastic control methods to regime-switching models. Under suitable conditions, we prove a verification theorem. We then apply the verification theorem to a power utility function and obtain, up to the solution of a system of coupled ordinary differential equations, an explicit solution of the value function and the optimal investment and consumption policies. We illustrate the impact of regime-switching on the optimal investment and consumption policies with numerical results and compare the results with the classical Merton problem that has only a single regime.

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

2018 ◽  
Vol 28 (09) ◽  
pp. 1699-1735 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Xiongtao Zhang
Keyword(s):  
Initial Data ◽  
Discrete Time ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Discrete Model ◽  
Stability Estimate ◽  
Functional Approach ◽  
Time Interval ◽  
Time Step ◽  
Time Model

We study a uniform-in-time convergence from the discrete-time (in short, discrete) Cucker–Smale (CS) model to the continuous-time CS model, which is valid for the whole time interval, as time-step tends to zero. Classical theory yields the convergence results which are valid only in any finite-time interval. Our uniform convergence estimate relies on two quantitative estimates “asymptotic flocking estimate” and “uniform[Formula: see text]-stability estimate with respect to initial data”. 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 [Formula: see text]-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.

scholarly journals $H_\infty$ State Estimation of Delayed Recurrent Memristive Neural Networks: continuous-time case and discrete-time case

2021 ◽  
Author(s):  
fangyuan Ma ◽  
Xingbao Gao
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Discrete Time ◽  
Continuous Time ◽  
Estimation Error ◽  
Linear Matrix ◽  
Memristive Neural Networks ◽  
Connection Weight ◽  
Discrete Time Case ◽  
The Given

This paper investigates the problem of $H_\infty$ state estimation of delayed recurrent memristive neural networks (DRMNNs) with both continuous-time and discrete-time cases. By utilizing Lyapunov-Krasovskii functional (LKF) and linear matrix inequalities (LMIs), two criterions are provided to guarantee the asymptotically stable of the estimation error systems with a $H_\infty$ performance. The connection weight parameters of DRMNNs are dealed with logical switching signals, which greatly reduces the computational complexity. The given conditions can be easily checked by solving LMIs, the obtained theoretical results are supported demonstrated by two numerical examples.

Hedging in discrete time under transaction costs and continuous-time limit

1999 ◽  
Vol 36 (01) ◽  
pp. 163-178 ◽  
Author(s):  
Pierre-F. Koehl ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Risky Asset ◽  
Market Model ◽  
Upper And Lower Bounds ◽  
Time Step ◽  
Proportional Transaction Costs ◽  
Call Options

We consider a discrete-time financial market model with L 1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs

2016 ◽  
Vol 03 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Foad Shokrollahi ◽  
Adem Kılıçman ◽  
Marcin Magdziarz
Keyword(s):  
Brownian Motion ◽  
Transaction Costs ◽  
Fractional Brownian Motion ◽  
Discrete Time ◽  
Empirical Studies ◽  
Time Step ◽  
Currency Option ◽  
Mixed Fractional Brownian Motion ◽  
Text Model ◽  
The Impact

This study investigates a new formula for option pricing with transaction costs in a discrete time setting. The value of the financial assets is based on time-changed mixed fractional Brownian motion [Formula: see text] model. The pricing method is obtained for European call option using the time-changed [Formula: see text] model in a discrete time setting. Particularly, the minimal value [Formula: see text] of an option respect to transaction costs is obtained. Furthermore, the new model for pricing currency option is presented by utilizing the time-changed [Formula: see text] model. In addition, the impact of time step [Formula: see text], Hurst parameter H and transaction costs [Formula: see text] are also investigated, which substantiate that these parameters play a significant role in our pricing formula. Finally, the empirical studies and the simulation findings corroborate the theoretical bases and indicate the time-changed [Formula: see text] is a satisfactory model.

scholarly journals Suboptimal Filtering of Networked Discrete-Time Systems with Random Observation Losses

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shouwan Gao ◽  
Pengpeng Chen
Keyword(s):  
Discrete Time ◽  
Estimation Error ◽  
Multiple Input Multiple Output ◽  
Discrete Time System ◽  
Time Step ◽  
Error Covariance ◽  
Mean Square Stability ◽  
Input Multiple Output ◽  
Multiple Measurements ◽  
Time Systems

This paper studies the remote filtering problem over a packet-dropping network. A general multiple-input-multiple-output (MIMO) discrete-time system is considered. The multiple measurements are sent over different communication channels every time step, and the packet loss phenomenon in every communication channel is described by an independent and identically distributed (i.i.d) Bernoulli process. A suboptimal filter is obtained which can minimize the mean squared estimation error. The convergence properties of the estimation error covariance are studied, and mean square stability of the suboptimal filter is proved under standard assumptions. A simulation example is exploited to demonstrate the effectiveness of the results.

Dynamical complexities of forced impacting systems

1992 ◽  
Vol 338 (1651) ◽  
pp. 547-556 ◽  
Keyword(s):  
Dynamical System ◽  
Discrete Time ◽  
Continuous Time ◽  
Linear Oscillator ◽  
Nonlinear Behaviour ◽  
Engineering Applications ◽  
Poincaré Maps ◽  
The Impact ◽  
Derivatives Of ◽  
Impacting Systems

The model of a forced linear oscillator with instantaneous impacts at one or two stops is discussed. The nonlinearities introduced by the instantaneous impact rule are sufficient to cause typical nonlinear behaviour. The impact rule is discontinuous, introducing discontinuities into discrete time Poincaré maps defined from the continuous time dynamical system. Discontinuities also exist in the derivatives of these maps. The implications of these discontinuities are discussed and their relevance to engineering applications is assessed with suggestions for further research.

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