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In this paper, we study a stochastic linear-quadratic control problem withrandom coefficients and regime switching on a horizon $[0,T\wedge\tau]$, where$\tau$ is a given random jump time for the underlying state process and $T$ isa constant. We obtain an explicit optimal state feedback control and explicitoptimal cost value by solving a system of stochastic Riccati equations (SREs)with jumps on $[0,T\wedge\tau]$. By the decomposition approach stemming fromfiltration enlargement theory, we express the solution of the system of SREswith jumps in terms of another system of SREs involving only Brownianfiltration on the deterministic horizon $[0,T]$. Solving the latter system isthe key theoretical contribution of this paper and we establish this for threedifferent cases, one of which seems to be new in the literature. These resultsare then applied to study a mean-variance hedging problem with randomparameters that depend on both Brownian motion and Markov chain. The optimalportfolio and optimal value are presented in closed forms with the aid of asystem of linear backward stochastic differential equations with jumps andunbounded coefficients in addition to the SREs with jumps.

Stochastic linear-quadratic control with a jump and regime switching on a random horizon