We investigate a model of a corporation which faces constant liability payments and which can choose a production/business policy from an available set of control policies with diierent expected proots and risks. The objective is to maximize the expected present value of the total dividend distributions. The main purpose of this paper is to deal with the impact of constraints on business activi...

This paper deals with reachability under unknown disturbances and incomplete information on the state space variables. The unknown disturbances are described by a special type of vector-valued stochastic Brownian input noise which depends on the values of vector-valued control. The control may be either unbounded or bounded by hard bounds. The reachabilty sets introduced here are deterministic....

We propose a continuous-time model of trading with heterogeneous beliefs. Risk-neutral agents face quadratic costs-of-carry on positions and thus their marginal valuation of the asset decreases with the size of their position, as it would be the case for risk-averse agents. In the equilibrium models of heterogeneous beliefs that followed the work by Harrison and Kreps, investors are risk-neutra...

We prove some Liouville properties for suband supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in OrnsteinUhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully n...

We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing classical work of Nerlove and Arrow [30]. In particular, we deal with controlled SDDE where the delay enters both the state and the control. Following ideas of Vinte...

We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is null on the target. The result applies to problems with the property that all trajectories sa...

We prove convergence of stationary distributions for the randomly forced Burgers and Hamilton-Jacobi equations in a limit when viscosity tends to zero. It turns out that for all values of the viscosity ν there exists a unique (up to an additive constant) solution to the randomly forced Hamilton-Jacobi equation which is extendible for all times. The main result follow from the convergence of the...

In this paper, we study the underlying geometry in the classical Hamilton-Jacobi equation. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear almost Poisson structure and a Hamiltonian function, both on the dual bundle (a Hamiltonian system). From them, it is possible to formulate the Hamilton-Jacobi e...

The paper proves a new uniqueness result for viscosity solutions of the Dirichlet problem for Hamilton-Jacobi equations of the form H(x; u; D x 0 u) = 0 in ; u = g on @; where is an open subset or R n and D x 0 u is the partial gradient of the scalar function u with respect to the rst n 0 variables (n 0 n). The main theorem states that there is a viscosity solution of the equation which is uniq...

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [31], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portf...