scholarly journals Dynamic Programming and Hamilton–Jacobi–Bellman Equations on Time Scales

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Dynamic Programming ◽  
Dynamic System ◽  
Time Scales ◽  
Discrete Time ◽  
Continuous Time ◽  
Stochastic Dynamic ◽  
Optimality Principle ◽  
Bellman Equations ◽  
Special Cases ◽  
Hamilton Jacobi Bellman

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman (HJB) equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

scholarly journals A Patchy Dynamic Programming Scheme for a Class of Hamilton--Jacobi--Bellman Equations

2012 ◽  
Vol 34 (5) ◽  
pp. A2625-A2649 ◽  
Author(s):  
Simone Cacace ◽  
Emiliano Cristiani ◽  
Maurizio Falcone ◽  
Athena Picarelli
Keyword(s):  
Dynamic Programming ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Dynamic Programming Scheme

scholarly journals Pinning Synchronization of Nonlinearly Coupled Complex Dynamical Networks on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fang-Di Kong
Keyword(s):  
Time Scales ◽  
Discrete Time ◽  
Control Strategy ◽  
Continuous Time ◽  
General Framework ◽  
Pinning Control ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Synchronization Problem

In this paper, we study the synchronization problem for nonlinearly coupled complex dynamical networks on time scales. To achieve synchronization for nonlinearly coupled complex dynamical networks on time scales, a pinning control strategy is designed. Some pinning synchronization criteria are established for nonlinearly coupled complex dynamical networks on time scales, which guarantee the whole network can be pinned to some desired state. The model investigated in this paper generalizes the continuous-time and discrete-time nonlinearly coupled complex dynamical networks to a unique and general framework. Moreover, two numerical examples are given for illustration and verification of the obtained results.

Dynamic Contest Games with Time Delays

2020 ◽  
Vol 22 (03) ◽  
pp. 1950017
Author(s):  
Akio Matsumoto ◽  
Ferenc Szidarovszky
Keyword(s):  
Time Scales ◽  
Characteristic Equation ◽  
Continuous Time ◽  
Local Stability ◽  
Time Delays ◽  
Delay Model ◽  
Delayed Information ◽  
Gradient Dynamics ◽  
Special Cases ◽  
Total Effort

Dynamic asymmetric contest games are examined under the assumption that the assessed value of the prize by each agent depends on the total effort of all agents, and each agent has only delayed information about the efforts of the competitors. Assuming gradient dynamics with continuous time scales, first the resulting one-delay model is investigated. Then, assuming additional delayed information about the agents’ own efforts, a two-delay model is constructed and analyzed. In both cases, first the characteristic equation is derived in the general case, and then two special cases are considered. First, symmetric agents are assumed and then general duopolies are examined. Conditions are derived for the local stability of the equilibrium including stability thresholds and stability switching curves.

scholarly journals OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT

2019 ◽  
Vol 22 (02) ◽  
pp. 1850059 ◽  
Author(s):  
WESTON BARGER ◽  
MATTHEW LORIG
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Price Impact ◽  
Trading Strategies ◽  
Impact Model ◽  
Optimal Liquidation ◽  
Special Cases ◽  
Time Price ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

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