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When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find…
In this paper, we consider the stochastic optimal control problem for jump diffusion systems with state constraints. In general, the value function of such problems is a discontinuous viscosity solution of the Hamilton-Jacobi-Bellman (HJB)…
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…
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…
In this paper, we explore a new class of stochastic control problems characterized by specific control constraints. Specifically, the admissible controls are subject to the ratcheting constraint, meaning they must be non-decreasing over…
This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but non-predicable parameter process, in addition to the…
Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB…
We consider an optimal dividend payout problem for an insurance company whose surplus follows the classical Cram\'er-Lundberg model. The dividend rate is subject to a ratcheting constraint (i.e., it must be nondecreasing over time), and the…
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…
Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…
This paper studies {a} mixed singular/switching stochastic control problem for a multidimensional diffusion with multiples regimes on a bounded domain. Using probabilistic, partial differential equation (PDE) and penalization techniques, we…
In this paper, we guarantee the existence and uniqueness (in the almost everywhere sense) of the solution to a Hamilton-Jacobi-Bellman (HJB) equation with gradient constraint and a partial integro-differential operator whose L\'evy measure…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is…
We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…
We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…
This study introduces a mathematical framework to investigate the viability and reachability of production systems under constraints. We develop a model that incorporates key decision variables, such as pricing policy, quality investment,…
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 paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…