Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

Average Continuous Control of Piecewise Deterministic Markov Processes

“…Davis [7,8], M.A.H. Dempster and J.J. Ye [9,10], Forwick, Schäl, and Schmitz [13], M. Schäl [22], A.A. Yushkevich [27,28]. The reader may consult the book by M.H.A.…”

“…A closely related paper to ours, but considering the discounted control case, is the paper by Forwick, Schäl, and Schmitz [13], which also considers unbounded costs and relaxed controls, and obtain sufficient conditions for the existence of ordinary feedback controls. However, in [13] the authors do not consider the long run average cost case neither the related limit problem associated to the vanishing approach.…”

“…However, in [13] the authors do not consider the long run average cost case neither the related limit problem associated to the vanishing approach. Besides, unlike in [13], we consider here boundary jumps and the control action space depending on the state variable. Note however that control on the flow is not considered here, while it was studied in [13].…”

Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

“…From a methodological point of view our analysis is also related to the literature on expected utility maximization or hedging for pure jump process such as Bäuerle and Rieder [10] or Kirch and Runggaldier [40]. Important contributions to the control theory of PDMPs include Davis [29], Dempster and Ye [31], Almudevar [4], Forwick et al [33], Bäuerle and Rieder [11], Costa and Dufour [25]. Viscosity solutions for PDMP control problems were previously considered in Davis and Farid [30].…”

Uniform Assymptotics in the Average Continuous Control of Piecewise Deterministic Markov Processes : Vanishing Approach

“…Piecewise deterministic Markov processes (PDMP) have been introduced by Davis [8], [10]. The literature on optimal control topics in connection to these processes is extremely wide ( [9], [20], [1], [11], [13], etc.). However, the cited papers deal mainly with infinite-horizon, discounted costs.…”