We offer a new proof of the maximum principle, by using the envelope theorem that is frequently used in the standard microeconomic theory. Copyright Springer-Verlag Berlin Heidelberg 2003

In this paper, we develop a dynamic model that captures the interaction between a firm’s cash reserves, the risk management policy and the profitability of a non-predictable irreversible investment opportunity. We consider a firm that has assets in place generating a stochastic cash-flow...

We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete...

The aim of this paper is to present a stochastic maximum principle for an optimal control problem of switching systems. It presents necessary conditions of optimality in the form of a maximum principle for stochastic switching systems, in which the dynamic of the constituent processes takes the...

We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a...

In this paper we analyze the discrete maximum principle (DMP) for a non-stationary diffusion–reaction problem solved by means of prismatic finite elements and θ-method. We derive geometric conditions on the shape parameters of prismatic partitions and time-steps which a priori guarantee...

We studied the optimal age- and season-specific sustainable harvesting policy for a fish population. We assumed that body weight, reproduction rate, and natural mortality of a fish vary with age. By assuming completely age- and season-specific harvesting, we can obtain a new, simple criterion...

We prove a maximum principle for local solutions of quasi-linear parabolic stochastic PDEs, with non-homogeneous second order operator on a bounded domain and driven by a space–time white noise. Our method based on an approximation of the domain and the coefficients of the operator, does not...

For α∈R, let pR(t,x,x) denote the diagonal of the transition density of the α-Bessel process in (0,1], killed at 0 and reflected at 1. As a function of x, if either α≥3 or α=1, then for t>0, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3.

We study backward stochastic differential equations (BSDEs) for time-changed Lévy noises when the time-change is independent of the Lévy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for linear BSDEs and a comparison principle. BSDEs naturally...