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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/10010324035
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/10010324042
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/10010324079
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/10010324095
In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with a highdimensional state space and complex dependence structure of the underlying Markov process with...
Persistent link: https://www.econbiz.de/10010276592