We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we sh...

The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments. We derive generalized...

Since we convert the original sequential problem into a collection of small problems, it is important to make sure that the solution to each of the small problems is actually optimal in the original problem. In other words, the optimal choice in each of the two-period problem must be globally optimal to justify the transformation. Richard Bellman, the inventor of the dynamic programming method,...

We prove a theorem of existence of time-optimal curves in the space of probability measures, a Dynamic Programming Principle, a controllability result and some comparisons between the classical and the generalized framework. A proper definition of viscosity solution, together with some approximation results, leaded us to prove that the generalization of the minimum time function solves a suitab...

In this paper, an event-triggered Reinforcement Learning (RL) method is proposed for the optimal attitude consensus of multiple rigid body networks with unknown dynamics. Firstly, error constructed through According to Bellman optimality principle, implicit form controller and corresponding Hamilton-Jacobi-Bellman (HJB) equations are obtained. Because augmented system, can be obtained directly ...

Time optimal control problems for systems with impulsive controls are investigated. Sufficient conditions for the existence of time optimal controls are given. A dynamical programming principle is derived and Lipschitz continuity of an appropriately defined value functional is established. The value functional satisfies a Hamilton-Jacobi-Bellman equation in the viscosity sense. A numerical exam...

In 1696, Johann Bernoulli solved the brachistochrone problem by an ingenious method of combining Fermat’s principle of minimum time, Snell’s law of refraction and “finite element” discretization. This appears to be the first application of a “direct method.” By taking the limits of these “broken-line solutions,” Bernoulli arrived at an equation for the cycloid. About fifty years later (1744), E...

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which hig...

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, existence and uniqueness theorem a solution for obtained using Lipschitz condition Banach contraction principle. Then, expression derived by mathematical induction. On basis, we obtain via Gronwall–Bellman inequality. Finally, two examples equations are given to explain our main results.

This paper describes the use of method selective, weighted morphological research by dividing inventics submorphologies to analyze equipment for biocompost production. The selective was used find optimal constructive solution which is then developed in research, design and testing an innovative piece equipment. Using Bellman's principle analysis, known solutions will be studied, their weighting...