Optimal Financial Benchmark Tracking in a Market with Unbounded Random Coefficients

We consider the problem of optimally tracking a financial benchmark in a market with random and possibly unbounded coefficients. This is an example of a stochastic linear-quadratic control problem with unbounded system and cost functional coefficients. We obtain the unique solution in an explicit closed-form as an affine state-feedback control. The coefficients of the control law are given in terms of two linear backward stochastic differential equations with unbounded coefficients, the solvability of which is also proved.