We compare the hybrid, stochastic, and differential semantics for stochastic Concurrent Constraint Programming, focussing on the exhibited behavior of models and their robustness. By investigating in detail two case studies, a circadian clock model and the Repressilator, we comment on the effect of the introduction of a limited amount of discreteness in the description of biological systems wit...

An optimal stochastic control problem is considered for systems with unbounded controls satisfying an integral constraint. It is shown that there exists an optimal control within the class of generalized controls leading to impulse actions. Applying an approach of time transformation, developed recently for deterministic systems, the original control problem is shown to be equivalent to an opti...

We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation, and obtain the upper hedging price ...

We propose an accelerated stochastic block coordinate descent algorithm for nonconvex optimization under sparsity constraint in the high dimensional regime. The core of our algorithm is leveraging both stochastic partial gradient and full partial gradient restricted to each coordinate block to accelerate the convergence. We prove that the algorithm converges to the unknown true parameter at a l...

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation GSARE that involves the MoorePenrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programmingSDPbased approach to study corresponding problems. Several relations among SDP compleme...

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are id...

This is a quantitative study of the valuation and hedging of dangerous options, options whose hedging strategies require unreasonable or risky short positions of the underlying instrument. We examine the valuation of many exotic options, when a shortselling constraint is imposed, as an example for Contingent Claims in Incomplete Markets. The valuation problem is known to be a stochastic control...

We study and solve a particular stochastic version of the Restricted Shortest Path Problem, the Stochastic Shortest Path Problem with Delay Excess Penalty. While arc costs are kept deterministic, arc delays are assumed to be normally distributed and a penalty per time unit occurs whenever the given delay constraint is not satisfied. The objective is to minimize the sum of path cost and total de...

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy that operates under this contraint and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optima...

In the discrete-time Envelope-Constrained filtering problem, the gain of the filter is minimised subject to the constraint that the filter output to a prescribed input fits into a given envelope. In this paper, a novel adaptive algorithm for solving this problem based on stochastic optimisation is presented. The algorithm is simple to implement on-line and convergence is demonstrated in numeric...