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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/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
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
In this paper we formulate the Risk Management Control problem in the interest rate area as a constrained stochastic portfolio optimization problem. The utility that we use can be any continuous function and based on the viscosity theory, the unique solution of the problem is guaranteed. The...
Persistent link: https://www.econbiz.de/10011552973
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In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is able to control its...
Persistent link: https://www.econbiz.de/10013165295