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In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to…
Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for…
We formulate and investigate a general stochastic control problem under a progressive enlargement of filtration. The global information is enlarged from a reference filtration and the knowledge of multiple random times together with…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
The generic case of pensions fund that it is not sufficiently auto financed and it is thoroughly maintained with an external financing effort is considered in this chapter. To represent the unrestricted reserves value process of this kind…
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave…
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
We develop a complete analysis of a general entry-exit-scrapping model. In particular, we consider an investment project that operates within a random environment and yields a payoff rate that is a function of a stochastic economic…
In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets.…
General theorems for existence and uniqueness of viscosity solutions for Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise…
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…
This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions ($c$ and $\chi$ not decreasing in time).…
We study an infinite horizon optimal stopping problem which arises naturally in the optimal timing of a firm/project sale or in the valuation of natural resources: the functional to be maximised is a sum of a discounted running reward and a…
We study a class of infinite horizon impulse control problems with execution delay when the dynamics of the system is described by a general adapted stochastic process. The problem is solved by means of probabilistic tools relying on the…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…