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This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
In this paper, we address the task of setting up an optimal production plan taking into account an uncertain demand. The energy system is represented by a system of hyperbolic partial differential equations (PDEs) and the uncertain demand…
We consider an infinite horizon optimal control problem for a pure jump Markov process $X$, taking values in a complete and separable metric space $I$, with noise-free partial observation. The observation process is defined as $Y_t =…
A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid…
We consider a periodic-review, fixed-lifetime perishable inventory control problem where demand is a general stochastic process. The optimal solution for this problem is intractable due to "curse of dimensionality". In this paper, we first…
We register a stochastic sequence affected by one disorder. Monitoring of the sequence is made in the circumstances when not full information about distributions before and after the change is available. The initial problem of disorder…
We study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final…
In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
Small-to-medium size enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this paper, we model a firm that can finance its inventory (ordered or manufactured) with loans in…
Consider a (logical) link between two distributed data centers with available bandwidth designated for both deadline-driven elastic traffic, such as for scheduled synchronization services, and profitable inelastic traffic, such as for…
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model…
We study a version of the stochastic control problem of minimizing the sum of running and controlling costs, where control opportunities are restricted to independent Poisson arrival times. Under a general setting driven by a general L\'evy…
All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk,…
Motivated by applications in online marketplaces such as ride-hailing, we study how strategic servers impact the system performance. We consider a discrete-time process in which, heterogeneous types of customers and servers arrive. Each…
Learning beneficial treatment allocations for a patient population is an important problem in precision medicine. Many treatments come with adverse side effects that are not commensurable with their potential benefits. Patients who do not…
In this paper we study the stochastic control problem of partially observed (multi-dimensional) stochastic system driven by both Brownian motions and fractional Brownian motions. In the absence of the powerful tool of Girsanov…