We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corre...

We consider the problem of optimal investment and consumption when the investment opportunity is represented by a hedge-fund charging proportional fees on profit. The value of the fund evolves as a geometric Brownian motion and the performance of the investment and consumption strategy is measured using discounted power utility from consumption on infinite horizon. The resulting stochastic cont...

We consider the optimal control of stochastic delayed systems with jumps, in which both the state and controls can depend on the past history of the system, for a value function which depends on the initial path of the process. We derive the Hamilton-Jacobi-Bellman equation and the associated verification theorem and prove a necessary and a sufficient maximum principles for such problems. Expli...

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...

The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.

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...