Related papers: Stochastic internal habit formation and optimality

In this paper we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed…

The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…

This paper aims to explore the relationship between maximum principle and dynamic programming principle for stochastic recursive control problem with random coefficients. Under certain regular conditions for the coefficients, the…

The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth…

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…

In this paper we study homogenization of a class of control problems in a stationary and ergodic random environment. This problem has been mostly studied in the calculus of variations setting in connection to the homogenization of the…

We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…

This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

This paper studies a composite problem involving the decision making of the optimal entry time and dynamic consumption afterwards. In stage-1, the investor has access to full market information subjecting to some information costs and needs…

This paper studies stochastic optimization problems and associated Bellman equations in formats that allow for reduced dimensionality of the cost-to-go functions. In particular, we study stochastic control problems in the…

The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…

We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…

We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

Dynamic decisions are pivotal to economic policy making. We show how existing evidence from randomized control trials can be utilized to guide personalized decisions in challenging dynamic environments with budget and capacity constraints.…

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…