Numerical methods for portfolio selection with bounded constraints
Journal of Computational and Applied Mathematics
Portfolio Choice under Space-Time Monotone Performance Criteria
SIAM Journal on Financial Mathematics
Journal of Computational Neuroscience
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This paper is devoted to the study of a stochastic linear-quadratic (LQ) optimal control problem where the control variable is constrained in a cone, and all the coefficients of the problem are random processes. Employing Tanaka's formula, optimal control and optimal cost are explicitly obtained via solutions to two extended stochastic Riccati equations (ESREs). The ESREs, introduced for the first time in this paper, are highly nonlinear backward stochastic differential equations (BSDEs), whose solvability is proved based on a truncation function technique and Kobylanski's results. The general results obtained are then applied to a mean-variance portfolio selection problem for a financial market with random appreciation and volatility rates, and with short-selling prohibited. Feasibility of the problem is characterized, and efficient portfolios and efficient frontier are presented in closed forms.