scholarly journals Lipschitz continuity and semiconcavity properties of the value function of a stochastic control problem

2010 ◽  
Vol 17 (6) ◽  
pp. 715-728 ◽  
Author(s):  
Rainer Buckdahn ◽  
Piermarco Cannarsa ◽  
Marc Quincampoix
Keyword(s):  
Control Problem ◽  
Stochastic Control ◽  
Value Function ◽  
Lipschitz Continuity ◽  
Stochastic Control Problem ◽  
The Value Function

scholarly journals Optimal dividend and reinsurance in the presence of two reinsurers

2016 ◽  
Vol 53 (2) ◽  
pp. 554-571 ◽  
Author(s):  
Mi Chen ◽  
Kam Chuen Yuen
Keyword(s):  
Control Problem ◽  
Transaction Costs ◽  
Stochastic Control ◽  
Value Function ◽  
Optimal Reinsurance ◽  
Stochastic Control Problem ◽  
Optimal Dividend ◽  
The Impact ◽  
The Value Function ◽  
Limit Diffusion

Abstract In this paper the optimal dividend (subject to transaction costs) and reinsurance (with two reinsurers) problem is studied in the limit diffusion setting. It is assumed that transaction costs and taxes are required when dividends occur, and that the premiums charged by two reinsurers are calculated according to the exponential premium principle with different parameters, which makes the stochastic control problem nonlinear. The objective of the insurer is to determine the optimal reinsurance and dividend policy so as to maximize the expected discounted dividends until ruin. The problem is formulated as a mixed classical-impulse stochastic control problem. Explicit expressions for the value function and the corresponding optimal strategy are obtained. Finally, a numerical example is presented to illustrate the impact of the parameters associated with the two reinsurers' premium principle on the optimal reinsurance strategy.

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.

scholarly journals A multidimensional singular stochastic control problem on a finite time horizon

2015 ◽  
Vol 69 (1) ◽  
Author(s):  
Marcin Boryc ◽  
Łukasz Kruk
Keyword(s):  
Control Problem ◽  
Stochastic Control ◽  
Finite Time ◽  
Time Horizon ◽  
Generalized Solution ◽  
Singular Stochastic Control ◽  
Stochastic Control Problem ◽  
Second Derivatives ◽  
Finite Time Horizon ◽  
The Value Function

AbstractA singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique

scholarly journals A multidimensional singular stochastic control problem on a finite time horizon

2015 ◽  
Vol 69 (1) ◽  
pp. 23
Author(s):  
Marcin Boryc ◽  
Łukasz Kruk
Keyword(s):  
Control Problem ◽  
Stochastic Control ◽  
Finite Time ◽  
Time Horizon ◽  
Generalized Solution ◽  
Singular Stochastic Control ◽  
Stochastic Control Problem ◽  
Second Derivatives ◽  
Finite Time Horizon ◽  
The Value Function

A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.

A Lower Bounding Linear Programming approach to the Perimeter Patrol Stochastic Control Problem

2012 ◽  
Author(s):  
Krishnamoorthy Kalyanam ◽  
Swaroop Darbha ◽  
Myoungkuk Park ◽  
Meir Pachter ◽  
Phil Chandler ◽  
...  
Keyword(s):  
Linear Programming ◽  
Control Problem ◽  
Stochastic Control ◽  
Programming Approach ◽  
Linear Programming Approach ◽  
Lower Bounding ◽  
Stochastic Control Problem
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