ON THE SINGULARITIES OF AN IMPULSIVE DIFFERENTIAL GAME ARISING IN MATHEMATICAL FINANCE

2006 ◽  
Vol 08 (02) ◽  
pp. 219-229 ◽  
Author(s):  
PIERRE BERNHARD
Keyword(s):  
Option Pricing ◽  
State Space ◽  
Differential Game ◽  
Impulse Control ◽  
Value Function ◽  
Mathematical Finance ◽  
The State

We investigate an impulse control differential game arising in a problem of option pricing in mathematical finance. In a previous paper, it was shown that its Value function in ℝ3 could be described as a pair of functions affine in one of the variables, joined on a 2D manifold. Depending on the regions of the state space, this manifold is either a dispersal one, an equivocal one or a 2D focal manifold. A pair of PDE's were derived for the focal part. Here we show that irrespective of the nature of this manifold, it has to satisfy this same set of PDE's.

THE VALUE FUNCTION OF A DIFFERENTIAL GAME WITH SIMPLE MOTIONS AND AN INTEGRO-TERMINAL COST

2018 ◽  
pp. 877-890
Author(s):  
Lyubov Gennad’evna Shagalova
Keyword(s):  
Differential Equation ◽  
State Space ◽  
Differential Game ◽  
Value Function ◽  
Piecewise Linear ◽  
The State ◽  
The Value Function

An antagonistic positional differential game of two persons is considered. The dynamics of the system is described by a differential equation with simple motions, and the payoff functional is integro-terminal. For the case when the terminal function and the Hamiltonian are piecewise linear, and the dimension of the state space is two, a finite algorithm for the exact construction of the value function is proposed.

The reliability of a large series system under Markov structure

1991 ◽  
Vol 23 (04) ◽  
pp. 894-908 ◽  
Author(s):  
M. T. Chao ◽  
James C. Fu
Keyword(s):  
Markov Chain ◽  
Structure Function ◽  
State Space ◽  
Value Function ◽  
The State ◽  
Regularity Conditions ◽  
Series System ◽  
Finite Markov Chain ◽  
General Series ◽  
Markov Structure

Let Y 1, · ··, Yn be a finite Markov chain and let f be a binary value function defined over the state space of the Y's. We study the reliability of general series system having the structure function φ (Y) = min {f(Y 1), · ··, f(Yn )} and show that, under certain regularity conditions, the reliability of the system tends to a constant c (1 ≥ c ≥ 0), where c often has the form c = exp {–λ}.

The reliability of a large series system under Markov structure

1991 ◽  
Vol 23 (4) ◽  
pp. 894-908 ◽  
Author(s):  
M. T. Chao ◽  
James C. Fu
Keyword(s):  
Markov Chain ◽  
Structure Function ◽  
State Space ◽  
Value Function ◽  
The State ◽  
Regularity Conditions ◽  
Series System ◽  
Finite Markov Chain ◽  
General Series ◽  
Markov Structure

Let Y1, · ··, Yn be a finite Markov chain and let f be a binary value function defined over the state space of the Y's. We study the reliability of general series system having the structure function φ (Y) = min {f(Y1), · ··, f(Yn)} and show that, under certain regularity conditions, the reliability of the system tends to a constant c (1 ≥ c ≥ 0), where c often has the form c = exp {–λ}.

scholarly journals Energy Management of Hybrid UAV Based on Reinforcement Learning

Electronics ◽  
2021 ◽  
Vol 10 (16) ◽  
pp. 1929
Author(s):  
Huan Shen ◽  
Yao Zhang ◽  
Jianguo Mao ◽  
Zhiwei Yan ◽  
Linwei Wu
Keyword(s):  
Reinforcement Learning ◽  
State Space ◽  
Energy Management ◽  
Internal Combustion Engines ◽  
Value Function ◽  
Learning Algorithm ◽  
The State ◽  
Combustion Engines ◽  
State Action ◽  
Action Value

In order to solve the flight time problem of Unmanned Aerial Vehicles (UAV), this paper proposes a set of energy management strategies based on reinforcement learning for hybrid agricultural UAV. The battery is used to optimize the working point of internal combustion engines to the greatest extent while solving the high power demand issues of UAV and the response problem of internal combustion engines. Firstly, the decision-making oriented hybrid model and UAV dynamic model are established. Owing to the characteristics of the energy management strategy (EMS) based on reinforcement learning (RL), which is an intelligent optimization algorithm that has emerged in recent years, the complex theoretical formula derivation is avoided in the modeling process. In terms of the EMS, a double Q learning algorithm with strong convergence is adopted. The algorithm separates the state action value function database used in derivation decisions and the state action value function-updated database brought by the decision, so as to avoid delay and shock within the convergence process caused by maximum deviation. After the improvement, the off-line training is carried out with a large number of flight data generated in the past. The simulation results demonstrate that the improved algorithm can show better performance with less learning cost than before by virtue of the search function strategy proposed in this paper. In the state space, time-based and residual fuel-based selection are carried out successively, and the convergence rate and application effect are compared and analyzed. The results show that the learning algorithm has stronger robustness and convergence speed due to the appropriate selection of state space under different types of operating cycles. After 120,000 cycles of training, the fuel economy of the improved algorithm in this paper can reach more than 90% of that of the optimal solution, and can perform stably in actual flight.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

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