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We provide an overview of an optimal control problem within a stochastic model of tumor growth, which includes drug application. The model comprises two stochastic differential equations (SDE) representing the diffusion of nutrient and drug…
Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
The paper addresses two variants of the stochastic shortest path problem ('optimize the accumulated weight until reaching a goal state') in Markov decision processes (MDPs) with integer weights. The first variant optimizes partial expected…
We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…
In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the…
We consider a robust asymptotic growth problem under model uncertainty in the presence of stochastic factors. We fix two inputs representing the instantaneous covariance for the asset price process $X$, which depends on an additional…
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…
This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…
We consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the…
This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…
This study investigates a stochastic production planning problem with a running cost composed of quadratic production costs and inventory-dependent costs. The objective is to minimize the expected cost until production stops when inventory…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
We consider a distribution logistics scenario where a shipping operator, managing a limited amount of resources, receives a stream of collection requests, issued by a set of customers along a booking time-horizon, that are referred to a…
This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A…
This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and…
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and…
We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval…