The illiquid market model HJB equations and characterization of the solution Power utility functions and numerical results

We consider a (microscopic) car-following model in traffic flow that can be seen as a semidiscrete scheme (discretization in space only) of a (macroscopic) Hamilton-Jacobi equation. For this discrete model, and for general velocity laws satisfying a strict chord inequality, we construct travelling solutions that are naturally associated to ”travelling shocks” for the conservation law derived fr...

In this paper we investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then...

Using a semi-discrete model that describes the heat transfer of a continuous casting process of steel, this paper is addressed to an optimal control problem of the continuous casting process in the secondary cooling zone with water spray control. The approach is based on the Hamilton–Jacobi–Bellman equation satisfied by the value function. It is shown that the value function is the viscosity so...

We discuss from a bi-Hamiltonian point of view the Hamilton–Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi–bi– Hamiltonian formulation of Pfaffian type. This property allows us to straightforwardly recover a set of separation variables for the corresponding Hamilton–Jacobi equation.

Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson’s stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schrödinger equation into a continuity equation and a modified Hamilton-Jacobi equation, fails for some quantum states. A very simple example is provid...

Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson’s stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schrödinger equation into a continuity equation and a modified Hamilton-Jacobi equation, fails for some quantum states. A very simple example is provid...

We formulate an Hamilton–Jacobi partial differential equation

We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi– Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.

In this paper we study a class of optimal dividend and investment problems assuming that the underlying reserve process follows the Sparre Andersen model, that is, the claim frequency is a “renewal” process, rather than a standard compound Poisson process. The main feature of such problems is that the underlying reserve dynamics, even in its simplest form, is no longer Markovian. By using the b...