Approximating the solution of a dynamic, stochastic multiple knapsack problem
Approximation of control problems involving ordinary and impulsive controls
Approximation of control problems involving ordinary and impulsive controls
In this paper we study an approximation scheme for a class of control problems involving an ordinary control v, an impulsive control u and its derivative . Adopting a space-time reparametrization of the problem which adds one variable to the state space we overcome some difficulties connected to the presence of . We construct an approximation scheme for that augmented system, prove that it converges to the value function of the augmented problem and establish an error estimates in L∞ for this approximation....
Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels
This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...
Approximation of the Snell envelope and american options prices in dimension one
We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
Approximation of the Snell Envelope and American Options Prices in dimension one
We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.
Boundary-value problems for Hamiltonian systems and absolute minimizers in calculus of variations.
Canonical greedy algorithms and dynamic programming
Classical solutions of linear regulator for degenerate diffusions.
Complex calculus of variations
In this article, we present a detailed study of the complex calculus of variations introduced in [M. Gondran: Calcul des variations complexe et solutions explicites d’équations d’Hamilton–Jacobi complexes. C.R. Acad. Sci., Paris 2001, t. 332, série I]. This calculus is analogous to the conventional calculus of variations, but is applied here to functions in . It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions...
Computing the value function for an optimal control problem.
Contrôle de processus de Markov
Controlled diffusion processes.
Convergence of optimal strategies in a discrete time market with finite horizon
A discrete-time financial market model with finite time horizon is considered, together with a sequence of investors whose preferences are described by a convergent sequence of strictly increasing and strictly concave utility functions. Existence of unique optimal consumption-investment strategies as well as their convergence to the limit strategy is shown.
Cooperative driving at isolated intersections based on the optimal minimization of the maximum exit time
Traditional traffic control systems based on traffic light have achieved a great success in reducing the average delay of vehicles or in improving the traffic capacity. The main idea of these systems is based on the optimization of the cycle time, the phase sequence, and the phase duration. The right-of-ways are assigned to vehicles of one or several movements for a specific time. With the emergence of cooperative driving, an innovative traffic control concept, Autonomous Intersection Management...
Decomposition of large-scale stochastic optimal control problems
In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline the framework...
Degenerate Eikonal equations with discontinuous refraction index
We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value...
Deterministic minimax impulse control in finite horizon: the viscosity solution approach
We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.
Deterministic optimal control via dynamic programming.
Dijkstra's algorithm revisited: the dynamic programming connexion