The optimal control problem is considered for linear stochastic systems with a singular cost. A new uniformly convex structure is formulated, and its consequences on the existence and uniqueness of optimal controls and on the uniform convexity of the value function are proved. In particular, the...

The following backward stochastic Riccati differential equation (BSRDE in short) is motivated, and is then studied. Some properties are presented. The existence and uniqueness of a global adapted solution to a BSRDE has been open for the case D i 6= 0 for more than two decades. Our recent...

We obtain the global existence and uniqueness result for a one-dimensional back- ward stochastic Riccati equation, whose generator contains a quadratic term of L (the second unknown component). This solves the one-dimensional case of Bismut-Peng's problem which was initially proposed by Bismut...

In both complete and incomplete markets we consider the problem of fulfilling a financial obligation xc as well as possible at time T if the initial capital is not sufficient to hedge xc. This introduces a new risk into the market and our main aim is to minimize this shortfall risk by making use...

We consider an optimal control problem for a one-dimensional Itô diffusion and a stochastic game of optimal stopping associated with it. Their value functions satisfy ... and an optimal control defines a saddle point for the game. This extends earlier results to the case of bounded variation...

The standard literature concerning intertemporal optimization in international finance is based upon certainty equivalence, and ignores risk and uncertainty. It therefore is not helpful concerning risk management and evaluation of the risk involved in the holding of international short-term...

An optimal control tool is described that is particularly useful for computing rules of large-scale models where users might otherwise have difficulty determining the state vector a priori and where the inversion of large, sparse matrices is involved. A small-scale demonstration is presented, as...