相关论文: Verification Theorems for Hamilton-Jacobi-Bellman …

This manuscript studies the Minkowski-Bellman equation, which is the Bellman equation arising from finite or infinite horizon optimal control of unconstrained linear discrete time systems with stage and terminal cost functions specified as…

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using…

Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various…

The purpose of this work is to introduce a notion of weak solution to the master equation of a potential mean field game and to prove that existence and uniqueness hold under quite general assumptions. Remarkably, this is achieved without…

We solve in mild sense Hamilton Jacobi Bellman equations, both in an infinite dimensional Hilbert space and in a Banach space, with lipschitz Hamiltonian and lipschitz continuous final condition, and asking only a weak regularizing property…

We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model…

Approximating the optimal value function $v^*$ for infinite-horizon, nonlinear, autonomous optimal control problems is both challenging and essential for synthesizing real-time optimal feedback. We develop an abstract optimal recovery…

We determine the optimal robust investment strategy of an individual who targets at a given rate of consumption and seeks to minimize the probability of lifetime ruin when she does not have perfect confidence in the drift of the risky…

This paper derives the Hamilton-Jacobi-Bellman equation of nonlinear optimal control problems for cost functions with fractional discount rate from the Bellman's principle of optimality. The fractional discount rate is described by…

We consider the optimal dividend problem in the so-called degenerate bivariate risk model under the assumption that the surplus of one branch may become negative. More specific, we solve the stochastic control problem of maximizing…

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…

In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…

This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…

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 investigate conditions of optimality for an infinite horizon control problem and consider their correspondence with the value function. Assuming Lipschitz continuity of the value function, we prove that sensitivity relations plus the…

We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach…

In an equity market model with "Knightian" uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative…

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…

A learning technique for finite horizon optimal control problems and its approximation based on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is involved when the feedback law is constructed by…

This work investigates the optimal control problem for reflected McKean-Vlasov SDEs and the viscosity solutions to Hamilton-Jacobi-Bellman(HJB) equations on the Wasserstein space in terms of intrinsic derivative. It follows from the flow…