Related papers: Equilibrium policies when preferences are time inc…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post…
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic…
In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance,…
Experience replay is a core ingredient of modern deep reinforcement learning, yet its benefits in policy optimization are poorly understood beyond empirical heuristics. This paper develops a novel theoretical framework for experience replay…
We formulate an equilibrium model of intraday trading in electricity markets. Agents face balancing constraints between their customers consumption plus intraday sales and their production plus intraday purchases. They have continuously…
In several socioeconomic-critical decision-making settings, such as fair resource allocation, climate policy, or AI alignment, multiple principals interact within a common arena. While it is well established that these principals may have…
We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework…
Having fixed capacities, homogeneous products and price sensitive customer purchase decision are primary distinguishing characteristics of numerous revenue management systems. Even with two or three rivals, competition is still highly…
We study the optimal investment-consumption problem for a member of defined contribution plan during the decumulation phase. For a fixed annuitization time, to achieve higher final annuity, we consider a variable consumption rate. Moreover,…
We study the policy evaluation problem in multi-agent reinforcement learning, modeled by a Markov decision process. In this problem, the agents operate in a common environment under a fixed control policy, working together to discover the…
We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod…
This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
In this paper, we focus on formal synthesis of control policies for finite Markov decision processes with non-negative real-valued costs. We develop an algorithm to automatically generate a policy that guarantees the satisfaction of a…
In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…
We study the interaction between strategy, heterogeneity and growth in a two-agent model of capital accumulation. Preferences are represented by recursive utility functions with decreasing marginal impatience. The stationary equilibria of…
In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our…
We consider a general time-inconsistent stochastic linear-quadratic differential game. The time-inconsistency arises from the presence of quadratic terms of the expected state as well as state-dependent term in the objective functionals. We…
In this paper, we investigate the effects of applying generalised (non-exponential) discounting on a long-run impulse control problem for a Feller-Markov process. We show that the optimal value of the discounted problem is the same as the…