We consider a robust switching control problem. The controller only observes the evolution of the state process, and thus uses feedback (closed-loop) switching strategies, a non standard class of switching controls introduced in this paper. The adverse player (nature) chooses open-loop controls that represent the so-called Knightian uncertainty, i.e., misspecifications of the model. The (half) ...

We consider an optimal control problem of linear stochastic integro-differential equation with conic constraints on the phase variable and the control of singular-regular type. Our setting includes consumption-investment problems for models of financial markets in the presence of proportional transaction costs where that the prices are geometric Lévy processes and the investor is allowed to tak...

This paper describes two explicit couplings of standard Brownian motions B and V , which naturally extend the mirror coupling and the synchronous coupling and respectively maximise and minimise (uniformly over all time horizons) the coupling time and the tracking error of two regime-switching martingales. The generalised mirror coupling minimises the coupling time of the two martingales while s...

The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniqu...

Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy ...

In various settings time consistency in dynamic programming has been addressed by many authors going all the way back to original developments by Richard Bellman. The basic idea of the involved dynamic principle is that a policy designed at the first stage, before observing realizations of the random data, should not be changed at the later stages of the decision process. This is a rather vague...

We consider a stochastic transportation problem between two prescribed probability distributions (a source and target) over processes with general drift dependence free end times. First, in order to establish dual principle, we associate equivalent formulations of the primal guarantee its convexity lower semi-continuity respect target distributions. exhibit an Eulerian formulation, whose variat...

There are two useful ways to extend nonlinear partial differential inequalities of second order: one uses viscosity theory and the other uses the theory of distributions. This paper considers the convex situation where both extensions can be applied. The main result is that under a natural “second-order completeness” hypothesis, the two sets of extensons are isomorphic, in a sense that is made ...

The emergence in the past decade of the Bellman function method as a powerful and versatile harmonic analysis technique has been characterized by rapid theoretical development on the one hand and somewhat ad hoc, if effective, approaches to some problems on the other. From the groundbreaking applications in [NTV1, NT, NTV2], which put the method on the map, to the concerted effort at tracing it...