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This paper deals with a family of stochastic control problems in Hilbert spaces which arises in typical applications (such as boundary control and control of delay equations with delay in the control) and for which is difficult to apply the…
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is…
In the last decades, control problems with infinite horizons and discount factors have become increasingly central not only for economics but also for applications in artificial intelligence and machine learning. The strong links between…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
We study a family of stochastic control problems arising in typical applications (such as boundary control and control of delay equations with delay in the control) with the ultimate aim of finding solutions of the associated HJB equations,…
In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates…
This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution…
Motivated by a control problem of a certain queueing network we consider a control problem where the dynamics is constrained in the nonnegative orthant $\mathbb{R}_+$ of the $d$-dimensional Euclidean space and controlled by the reflections…
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider…
We derive the explicit solutions to singular stochastic control problems of the monotone follower type with (a) an expected discounted criterion, (b) an expected ergodic criterion and (c) a pathwise ergodic criterion. These problems have…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
We study a time-inconsistent singular control problem originating from irreversible reinsurance decisions with non-exponential discount. A novel definition of equilibrium for time-inconsistent singular control problems is introduced. For…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called "fuel". In contrast to the vast majority of existing…
In this paper we deal with the problem of existence of a smooth solution of the Hamilton-Jacobi-Bellman-Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A…
This paper studies an optimal dividend problem with a drawdown constraint in a Brownian motion model, requiring the dividend payout rate to remain above a fixed proportion of its historical maximum. This leads to a path-dependent stochastic…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…