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This paper considers optimal (minimizing) control of stochastic linear quadratic regulators (LQRs). The assumption that the control weight costs must be positive definite, inherited from the deterministic case, has been taken for granted in the literature. It is, however, shown in this paper that some stochastic LQR problems with indefinite (in particular,(More)
This paper is concerned with mean-variance portfolio selection problems in continuous-time under the constraint that short-selling of stocks is prohibited. The problem is formulated as a stochastic optimal linear-quadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take(More)
— We study a discrete-time version of Markowitz's mean-variance portfolio selection problem where the market parameters depend on the market mode (regime) that jumps among a finite number of states. The random regime switching is delineated by a finite-state Markov chain, based on which a discrete-time Markov modulated portfolio selection model is(More)
The object of this paper is to study the mean–variance portfolio optimization in continuous time. Since this problem is time inconsistent we attack it by placing the problem within a game theoretic framework and look for subgame perfect Nash equilibrium strategies. This particular problem has already been studied in [2] where the authors assumed a constant(More)
We correct the proof of Theorem 4. by imposing additional conditions on the viscosity subsolution U. The proof of the stochastic verification theorem, Theorem 4.1 of [3], is not correct without additional assumptions on the function U there, which is a viscosity subsolution of the underlying HJB equation. with a gap in its proof, and [3] was an attempt to(More)
We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential(More)
We investigate a model of a corporation which faces constant liability payments and which can choose a production/business policy from an available set of control policies with diierent expected proots and risks. The objective is to maximize the expected present value of the total dividend distributions. The main purpose of this paper is to deal with the(More)