Time-Inconsistent Stochastic LQ Problem with Regime Switching

Time-inconsistent stochastic linear-quadratic optimal control problem under non-Markovian regime-switching jump-diffusion model

“…Now, we go on to proof the equality in (28). Let u t,ε,v (•) be defined by the spike variation (23) for some fixed arbitrarily v ∈ L 2…”

“…Ft Ω, R d , let {u t,εj ,v (•)} j≥1 be the sequence of controls defined by the spike variation (23) for some fixed arbitrarily v ∈ L 2…”

“…The authors obtained an analytical expression of the open-loop optimal control by means of the unique solvability of the corresponding stochastic Riccati system. For time-inconsistent SLQ problems with regime-switching, one can refer to the series of recent papers [34], [4] and [23]. Specifically, Wei [34] investigated a general class of non-exponential discounting time-inconsistent stochastic control problems for diffusion processes with regimeswitching.…”

“…Bouaicha et al [4] explored the open-loop equilibrium solution by using a variational method. Finally, Si et al [23] addressed the discrete-time framework and characterized the open-loop equilibrium control via a regime-switching forward-backward stochastic difference equation. Nevertheless, the regime-switching SLQ models considered in the aforementioned references are of the Markovian type (i.e., the weighting coefficients only depend on the current state of the Markov chain).…”