Showing 1 - 8 of 8
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...
Persistent link: https://www.econbiz.de/10011543567
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...
Persistent link: https://www.econbiz.de/10011543597
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...
Persistent link: https://www.econbiz.de/10011543687
It is well known that backward stochastic differential equations (BSDEs) stem from the study on the Pontryagin type maximum principle for optional stochastic control. A solution of a BSDE hits a given terminal value (which is a random variable) by virtue of an additional martingale term and an...
Persistent link: https://www.econbiz.de/10011543852
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...
Persistent link: https://www.econbiz.de/10011544520
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.
Persistent link: https://www.econbiz.de/10011544985
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...
Persistent link: https://www.econbiz.de/10011545021
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...
Persistent link: https://www.econbiz.de/10011545181