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A System of BSDEs with Singular Terminal Values Arising in Optimal Liquidation with Regime Switching (2412.19058v2)
Published 26 Dec 2024 in q-fin.MF, math.OC, and math.PR
Abstract: We study a stochastic control problem with regime switching arising in an optimal liquidation problem with dark pools and multiple regimes. The new feature of this model is that it introduces a system of BSDEs with jumps and with singular terminal values, which appears in literature for the first time. The existence result for this system is obtained. As a result, we solve the stochastic control problem with regime switching. More importantly, the uniqueness result of this system is also obtained, in contrast to merely minimal solutions established in most related literature.