On Regularized Optimal Execution Problems and Their Singular Limits

We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that multidimensional Markovian stochastic factor drives of them. Moreover, model indirect costs as temporary price impact, stipulating power law to relate it agent's turnover rate. first analyse regularized setting, admissible strategies do not ensure complete initial inventory. prove existence uniqueness continuous bounded viscosity solution Hamilton–Jacobi–Bellman equation, whence obtain characterization optimal trading As byproduct proof, numerical algorithm. Then, constrained problem, must guarantee trader. solve through monotonicity argument, obtaining strategy singular limit counterparts.