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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)
Novel substituted indolocarbazoles were synthesized, and their kinase inhibitory capability was evaluated in vitro. 6-Substituted indolocarbazoles 4 were found to be potent and selective D1/CDK4 inhibitors. 4d and 4h exhibited potent and ATP-competitive D1/CDK4 activities with IC50 values of 76 and 42 nM, respectively. Both compounds had high selectivity(More)
Rosmarinic acid (RA) and lithospermic acid B (LAB) are two typical phenolic acids with significant bioactivities that may contribute to the therapeutic effects of Salvia miltiorrhiza. Precise knowledge of the biosynthetic pathway leading to RA and LAB is a necessary prerequisite to optimize the production of important phenolic compounds in S. miltiorrhiza.(More)
I study the provision of incentives in dynamic moral hazard models with hidden actions and possibly hidden states. I characterize implementable contracts by establishing the applicability of the first-order approach to contracting. Implementable contracts are history dependent, but can be written recursively with a small number of state variables. When the(More)
This paper is concerned with mean-variance portfolio selection problems in continuoustime 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 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)
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)
This paper is concerned with stock loan valuation in which the underlying stock price is dictated by geometric Brownian motion with regime switching. The stock loan pricing is quite different from that for standard American options because the associated variational inequalities may have infinitely many solutions. In addition, the optimal stopping time(More)