We present a numerical approach for the timeoptimal feedback control of an advection-reaction-diffusion model. Our approach is composed by three main building blocks: approximation of the abstract system dynamics, feedback computation based on dynamic programming and state observation. For the approximation of the abstract dynamics, we consider a finite element semi-discretization in space, lea...

We study the problem of minimal initial capital needed in order to hedge a European contingent claim without risk. The nancial market presents incompleteness arising from two sources: stochastic volatility and portfolio constraints described by a closed convex set. In contrast with previous literature which uses the dual formulation of the problem, we use an original dynamic programming princip...

We summarize the recently-developed framework of linearly-solvable stochastic optimal control. Using an exponential transformation, the (Hamilton-Jacobi) Bellman equation for such problems can bemade linear, giving rise to efficient numericalmethods. Extensions to game theory are also possible and lead to linear Isaacs equations. The key restriction that makes a stochastic optimal control probl...

In this paper, we propose an exact solution method to generate fair policies in Multiobjective Markov Decision Processes (MMDPs). MMDPs consider n immediate reward functions, representing either individual payoffs in a multiagent problem or rewards with respect to different objectives. In this context, we focus on the determination of a policy that fairly shares regrets among agents or objectiv...

Abstract A numerical scheme for solving high-dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined. The scheme rests on the interpretation of the corresponding Hamilton-Jacobi-Bellman equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem...

We consider a mathematical framework of finite state Markov Decision Processes (MDPs) in which a weighted sum of the classical state-dependent cost and the transfer entropy from the state random process to the control random process is minimized. Physical interpretations of the considered MDPs are provided in the context of networked control systems theory and non-equilibrium thermodynamics. Ba...

This paper is concerned with Sobolev weak solution of Hamilton-Jacobi-Bellman (HJB) equation. This equation is derived from the dynamic programming principle in the study of the stochastic optimal control problem. Adopting Doob-Meyer decomposition theorem as one of main tool, we prove that the optimal value function is the unique Sobolev weak solution of the corresponding HJB equation. For the ...

In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with a high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea behind the algorithms is to simulate a set of trajectories unde...

Insurance companies are increasingly facing losses that have heavy exposure to capital market risks through the issuance of equity-linked insurance policies. In this paper, we determine the continuous premium rate that an insurer charges via the principle of equivalent utility. Using exponential utility, we obtain the resulting premium rate in terms of a risk-neutral expectation. We also consid...

Dynamic optimization problems can be numerically solved by direct, indirect and HamiltonJacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant diff...