The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from one or more independent Poisson processes. Optimal behavior in such a setup (e.g., optimal consumption) is usually determined by employing the Hamilton-Jacobi-Bellman...

Alan Greenspan's paper (March 2010) presents his retrospective view of the crisis. His theme has several parts. First, the housing price bubble, its subsequent collapse and the financial crisis were not predicted either by the market, the FED, the IMF or the regulators in the years leading to...

Multi-dimensional backward stochastic Riccati differential equations (BSRDEs in short) are studied. A closed property for solutions of BSRDEs with respect to their coefficients is stated and is proved for general BSRDEs, which is used to obtain the existence of a global adapted solution to some...

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...

We review the relations between adjoints of stochastic control problems with the derivative of the value function, and the latter with the value function of a stopping problem. These results are applied to the pricing of contingent claims.

We analyze the life cycle consumption choice model for multiple goods, focusing on the distinction between durables and perishables. As an approximation of the fact that rather high transaction costs and market imperfections prevail in markets for used durables, we assume that investment in...