A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

References

• [1] Acciaio B, Backhoff J, Carmona R (2019) Extended mean field control problems: Stochastic maximum principle and transport perspective. SIAM J. Control Optim. 57(6):3666–3693.Crossref, Google Scholar
• [2] Ackermann J, Kruse T, Urusov M (2021) Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models. Finance Stochastics 25(4):757–810.Crossref, Google Scholar
• [3] Ackermann J, Kruse T, Urusov M (2022) Reducing Obizhaeva-Wang type trade execution problems to LQ stochastic control problems. Preprint, submitted June 8, https://doi.org/10.48550/arXiv.2206.03772.Google Scholar
• [4] Alfonsi A, Blanc P (2016) Dynamic optimal execution in a mixed-market-impact Hawkes price model. Finance Stochastics 20(1):183–218.Crossref, Google Scholar
• [5] Alfonsi A, Fruth A, Schied A (2010) Optimal execution strategies in limit order books with general shape functions. Quant. Finance 10(2):143–157.Crossref, Google Scholar
• [6] Almgren R, Chriss N (2001) Optimal execution of portfolio transactions. J. Risk 3(2):5–40.Crossref, Google Scholar
• [7] Ankirchner S, Jeanblanc M, Kruse T (2014) BSDEs with singular terminal condition and a control problem with constraints. SIAM J. Control Optim. 52(2):893–913.Crossref, Google Scholar
• [8] Bank P (2005) Optimal control under dynamic fuel constraint. SIAM J. Control Optim. 44(4):1529–1541.Crossref, Google Scholar
• [9] Bank P, El Karoui N (2004) A stochastic representation theorem with applications to optimization and obstacle problems. Ann. Probab. 32(1B):1030–1067.Crossref, Google Scholar
• [10] Bank P, Riedel F (2001) Optimal consumption choice with intertemporal substitution. Ann. Appl. Probab. 11(3):750–788.Crossref, Google Scholar
• [11] Becherer D, Bilarev T, Frentrup P (2019) Stability for gains from large investors’ strategies in M1/J1 topologies. Bernoulli 25(2):1105–1140.Crossref, Google Scholar
• [12] Bertsimas D, Lo A (1998) Optimal control of execution costs. J. Financial Marketing 1(1):1–50.Crossref, Google Scholar
• [13] Brunnermeier M, Pedersen L (2005) Predatory trading. J. Finance 60(4):1825–1863.Crossref, Google Scholar
• [14] Campi L, De Angelis T, Ghio M, Livieri G (2022) Mean-field games of finite-fuel capacity expansion with singular controls. Ann. Appl. Probab. 32(5):3674–3717.Google Scholar
• [15] Cao H, Guo X (2022) MFGs for partially reversible investment. Stochastic Processes Their Appl. 150:995–1014.Google Scholar
• [16] Cao H, Dianetti J, Ferrari G (2022) Stationary discounted and ergodic mean field games of singular control. Math. Oper. Res. 48(4):1871–1898.Link, Google Scholar
• [17] Carlin B, Lobo M, Viswanathan S (2007) Episodic liquidity crises: Cooperative and predatory trading. J. Finance 62(5):2235–2274.Crossref, Google Scholar
• [18] Carmona R, Webster K (2019) The self-financing equation in limit order book markets. Finance Stochastics 23(3):729–759.Crossref, Google Scholar
• [19] Cartea A, Jaimungal S (2016) Incorporating order-flow into optimal execution. Math. Financial Econom. 10(3):339–364.Crossref, Google Scholar
• [20] Cartea A, Jaimungal S, Ricci J (2018) Algorithmic trading, stochastic control, and mutually exciting processes. SIAM Rev. 60(3):673–703.Crossref, Google Scholar
• [21] Cayé T, Muhle-Karbe J (2016) Liquidation with self-exciting price impact. Math. Financial Econom. 10(1):15–28.Crossref, Google Scholar
• [22] Chen N, Kou S, Wang C (2018) A partitioning algorithm for markov decision processes with applications to market microstructure. Management Sci. 64(2):784–803.Link, Google Scholar
• [23] Chen Y, Horst U, Tran H (2021) Optimal trade execution under endogenous order flow. Preprint, submitted September 26, http://dx.doi.org/10.2139/ssrn.3933364.Google Scholar
• [24] Cosso A, Pham H (2019) Zero-sum stochastic differential games of generalized McKean–Vlasov type. J. Math. Pures Appl. 129:180–212.Crossref, Google Scholar
• [25] Dianetti J, Ferrari G (2021) Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls. Preprint, submitted March 15, https://doi.org/10.48550/arXiv.2103.08487.Google Scholar
• [26] Dianetti J, Ferrari G, Fischer M, Nendel M (2023) A unifying framework for submodular mean field games. Math. Oper. Res. 48(3):1679–1710.Google Scholar
• [27] Elie R, Moreau L, Possamaï D (2018) On a class of path-dependent singular stochastic control problems. SIAM J. Control Optim. 56(5):3260–3295.Crossref, Google Scholar
• [28] Fruth A, Schöneborn T, Urusov M (2014) Optimal trade execution and price manipulation in order books with time-varying liquidity. Math. Finance 24(4):651–695.Crossref, Google Scholar
• [29] Fu G (2023) Extended mean field games with singular controls. SIAM J. Control Optim. 61(1):285–314.Crossref, Google Scholar
• [30] Fu G, Horst U (2017) Mean field games with singular controls. SIAM J. Control Optim. 55(6):3833–3868.Crossref, Google Scholar
• [31] Fu G, Horst U (2020) Mean-field leader-follower games with terminal state constraint. SIAM J. Control Optim. 58(4):2078–2113.Crossref, Google Scholar
• [32] Fu G, Hager P, Horst U (2023) Mean-field liquidation games with market drop-out. Preprint, submitted September 7, https://doi.org/10.48550/arXiv.2303.05783.Google Scholar
• [33] Fu G, Horst U, Xia X (2022) Portfolio liquidation games with self-exciting order flow. Math. Finance 32(4):1020–1065.Crossref, Google Scholar
• [34] Fu G, Graewe P, Horst U, Popier A (2021) A mean field game of optimal portfolio liquidation. Math. Oper. Res. 46(4):1250–1281.Link, Google Scholar
• [35] Gârleanu N, Pedersen L (2016) Dynamic portfolio choice with frictions. J. Econom. Theory 165:487–516.Crossref, Google Scholar
• [36] Gatheral J (2011) No-dynamic-arbitrage and market impact. Quant. Finance 10(7):749–759.Crossref, Google Scholar
• [37] Gatheral J, Schied A (2011) Optimal trade execution under geometric Brownian motion in the Almgren and Chriss framework. Internat. J. Theoret. Appl. Finance 14(3):353–368.Crossref, Google Scholar
• [38] Graewe P, Horst U (2017) Optimal trade exection with instantaneous price impact and stochastic resilience. SIAM J. Control Optim. 55(6):3707–3725.Crossref, Google Scholar
• [39] Graewe P, Horst U, Qiu J (2015) A non-Markovian liquidation problem and backward SPDEs with singular terminal conditions. SIAM J. Control Optim. 53(2):690–711.Crossref, Google Scholar
• [40] Guo X, Xu R (2020) Stochastic games for fuel followers problem: N vs MFG. SIAM J. Control Optim. 57(1):659–692.Crossref, Google Scholar
• [41] Guo X, Pham H, Wei X (2023) Itô’s formula for flow of measures on semimartingales. Stochastic Processes Their Appl. 159:350–390.Google Scholar
• [42] Hafayed M (2013) A mean-field necessary and sufficient conditions for optimal singular stochastic control. Comm. Math. Statist. 1(4):417–435.Crossref, Google Scholar
• [43] Hawkes A, Oakes D (1974) A cluster process representation of a self-exciting process. J. Appl. Probab. 11(3):493–503.Crossref, Google Scholar
• [44] Horst U, Kivman E (2021) Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies. Preprint, submitted March 10, https://doi.org/10.48550/arXiv.2103.05957.Google Scholar
• [45] Horst U, Naujokat F (2014) When to cross the spread? Trading in two-sided limit order books. SIAM J. Financial Math. 5(1):278–315.Crossref, Google Scholar
• [46] Horst U, Xia X (2019) Multidimensional optimal trade execution under stochastic resilience. Finance Stochastics 4(23):889–923.Crossref, Google Scholar
• [47] Horst U, Xia X, Zhou C (2022) Portfolio liquidation under factor uncertainty. Ann. Appl. Probab. 32(1):80–123.Crossref, Google Scholar
• [48] Hu Y, Øksendal B, Sulem A (2017) Singular mean-field control games. Stochastic Anal. Appl. 35(5):823–851.Crossref, Google Scholar
• [49] Kohlmann M, Tang S (2003) Multidimensional backward stochastic Riccati equations and applications. SIAM J. Control Optim. 41(6):1696–1721.Google Scholar
• [50] Kruse T, Popier A (2016) Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting. Stochastic Processes Their Appl. 126(9):2554–2592.Google Scholar
• [51] Lorenz C, Schied A (2013) Drift dependence of optimal trade execution strategies under transient price impact. Finance Stochastics 17(4):743–770.Crossref, Google Scholar
• [52] Muhle-Karbe J, Wang Z, Webster K (2022) Stochastic liquidity as a proxy for nonlinear price impact. Preprint, submitted January 1, http://dx.doi.org/10.2139/ssrn.4286108.Google Scholar
• [53] Neuman E, Voß M (2022) Optimal signal-adaptive trading with temporary and transient price impact. SIAM J. Financial Math. 13(2):551–575.Crossref, Google Scholar
• [54] Obizhaeva A, Wang J (2013) Optimal trading strategy and supply/demand dynamics. J. Financial Marketing 16(1):1–32.Crossref, Google Scholar
• [55] Popier A, Zhou C (2019) Second order BSDE under monotonicity condition and liquidation problem under uncertainty. Ann. Appl. Probab. 29(3):1685–1739.Crossref, Google Scholar
• [56] Predoiu S, Shaikhet G, Shreve S (2011) Optimal execution in a general one-sided limit-order book. SIAM J. Financial Math. 2(1):183–212.Crossref, Google Scholar
• [57] Protter PE (2005) Stochastic Integration and Differential Equations (Springer, Berlin).Crossref, Google Scholar
• [58] Schied A, Schöneborn T (2009) Liquidation in the face of adversity: Stealth vs. sunshine trading. Preprint, submitted March 18, http://dx.doi.org/10.2139/ssrn.1007014.Google Scholar