Topic
Bellman equation
About: Bellman equation is a research topic. Over the lifetime, 5884 publications have been published within this topic receiving 135589 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This paper derives explicit closed form solutions for the efficient frontier and optimal investment strategy for the dynamic mean-variance portfolio selection problem under the constraint of a higher borrowing rate using the Hamilton-Jacobi-Bellman equation in a stochastic piecewise linear-quadratic control framework.
118 citations
TL;DR: An optimal consumption and investment model in continuous time is considered, which is an extension of the original Merton's problem, and the asset prices are affected by correlated economic factors, modelled as diffusion processes.
Abstract: We consider an optimal consumption and investment model in continuous time, which is an extension of the original Merton's problem. In the proposed model, the asset prices are affected by correlated economic factors, modelled as diffusion processes. Writing the value function in a special form, it can be seen that another optimal control problem is involved and studying its associated HJB equation smoothness properties of the original value function can be derived as well as optimal policies.
118 citations
TL;DR: In this article, the trajectories of piecewise deterministic Markov processes are solved by an ordinary (vector)differential equation with possible random jumps between the different integral curves, and both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting of continuous, jump and terminal costs.
Abstract: The trajectories of piecewise deterministic Markov processes are solutions of an ordinary (vector)differential equation with possible random jumps between the different integral curves. Both continuous deterministic motion and the random jumps of the processes are controlled in order to minimize the expected value of a performance functional consisting of continuous, jump and terminal costs. A limiting form of the Hamilton-Jacobi-Bellman partial differential equation is shown to be a necessary and sufficient optimality condition. The existence of an optimal strategy is proved and acharacterization of the value function as supremum of smooth subsolutions is also given. The approach consists of imbedding the original control problem tightly in a convex mathematical programming problem on the space of measures and then solving the latter by dualit
118 citations
TL;DR: In this paper, the optimal control of general stochastic McKean-Vlasov equation under common noise is studied. But the authors focus on the control of the value function in the Wasserstein space of probability measures, which is proved from a flow property of the controlled state process.
Abstract: We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field interaction under common noise. Our first main result is to state a dynamic programming principle for the value function in the Wasserstein space of probability measures, which is proved from a flow property of the conditional law of the controlled state process. Next, by relying on the notion of differentiability with respect to probability measures due to P.L. Lions [32], and Ito's formula along a flow of conditional measures, we derive the dynamic programming Hamilton-Jacobi-Bellman equation, and prove the viscosity property together with a uniqueness result for the value function. Finally, we solve explicitly the linear-quadratic stochastic McKean-Vlasov control problem and give an application to an interbank systemic risk model with common noise.
117 citations
TL;DR: In this article, a linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an exponential substitution, into the dynamic programming equation of an optimal stochastic control problem.
Abstract: A linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an exponential substitution. into the dynamic programming equation of an optimal stochastic control problem. This substitution is applied to obtain results about the rate of decay as of solutions p(x,t)to the pathwise filter equation, and for solutions of the corresponding Zakai equation
117 citations