scholarly journals Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Peimin Chen ◽  
Bo Li
Keyword(s):  
Boundary Condition ◽  
Variational Inequalities ◽  
Stochastic Control ◽  
Optimization Problem ◽  
Value Function ◽  
The State ◽  
Tax Rate ◽  
Nonzero Boundary ◽  
The Value Function ◽  
Nonzero Boundary Condition

In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy.

scholarly journals EVOLUTION OF AMERICAN OPTION VALUE FUNCTION ON A DIVIDEND PAYING STOCK UNDER JUMP-DIFFUSION PROCESSES

2017 ◽  
Vol 2 (3) ◽  
pp. 212-221
Author(s):  
Рехман ◽  
Nazir Rekhman ◽  
Хуссейн ◽  
Zakir Khusseyn ◽  
Али ◽  
...  
Keyword(s):  
Variational Inequalities ◽  
Value Function ◽  
Diffusion Processes ◽  
Equivalent Form ◽  
Jump Diffusion ◽  
American Option ◽  
Option Value ◽  
Jump Diffusion Processes ◽  
Hedging Strategies ◽  
The Value Function

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

Geometric Asymptotic Approximation of Value Functions

2009 ◽  
Vol 9 (1) ◽  
Author(s):  
Axel Anderson
Keyword(s):  
Value Function ◽  
Payoff Function ◽  
The State ◽  
Second Derivative ◽  
Value Functions ◽  
State Variable ◽  
Specific Formula ◽  
Geometric Term ◽  
Dynamic Stochastic ◽  
The Value Function

This paper characterizes the behavior of value functions in dynamic stochastic discounted programming models near fixed points of the state space. When the second derivative of the flow payoff function is bounded, the value function is proportional to a linear function plus geometric term. A specific formula for the exponent of this geometric term is provided. This exponent continuously falls in the rate of patience.If the state variable is a martingale, the second derivative of the value function is unbounded. If the state variable is instead a strict local submartingale, then the same holds for the first derivative of the value function. Thus, the proposed approximation is more accurate than Taylor series approximation.The approximation result is used to characterize locally optimal policies in several fundamental economic problems.

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.

A quasilinear elliptic equation in ℝN

1996 ◽  
Vol 126 (5) ◽  
pp. 911-921 ◽  
Author(s):  
O. Alvarez
Keyword(s):  
Lower Bound ◽  
Elliptic Equation ◽  
Control Problem ◽  
Stochastic Control ◽  
Quasilinear Elliptic Equation ◽  
Value Function ◽  
Optimal Criterion ◽  
Hamilton Jacobi Bellman ◽  
Quasilinear Elliptic ◽  
The Value Function

A quasilinear elliptic equation in ℝN of Hamilton-Jacobi-Bellman type is studied. An optimal criterion for uniqueness which involves only a lower bound on the functions is given. The unique solution in this class is identified as the value function of the associated stochastic control problem.

scholarly journals A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lucas Izydorczyk ◽  
Nadia Oudjane ◽  
Francesco Russo
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Control Problem ◽  
Stochastic Control ◽  
Computational Efficiency ◽  
Value Function ◽  
Semilinear Pdes ◽  
Areas Of Interest ◽  
The Value Function

Abstract We propose a fully backward representation of semilinear PDEs with application to stochastic control. Based on this, we develop a fully backward Monte-Carlo scheme allowing to generate the regression grid, backwardly in time, as the value function is computed. This offers two key advantages in terms of computational efficiency and memory. First, the grid is generated adaptively in the areas of interest, and second, there is no need to store the entire grid. The performances of this technique are compared in simulations to the traditional Monte-Carlo forward-backward approach on a control problem of thermostatic loads.

Nested variational inequalities and related optimal starting–stopping problems

1992 ◽  
Vol 29 (01) ◽  
pp. 104-115 ◽  
Author(s):  
M. Sun
Keyword(s):  
Differential Equation ◽  
Variational Inequalities ◽  
Stochastic Differential Equation ◽  
Differential Game ◽  
Diffusion Model ◽  
Value Function ◽  
Optimal Strategies ◽  
Stochastic Differential Game ◽  
The Value Function

This paper introduces several versions of starting-stopping problem for the diffusion model defined in terms of a stochastic differential equation. The problem could be regarded as a stochastic differential game in which the player can only decide when to start the game and when to quit the game in order to maximize his fortune. Nested variational inequalities arise in studying such a problem, with which we are able to characterize the value function and to obtain optimal strategies.

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