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.