On Singular Control for Lévy Processes

References

• [1] Asmussen S, Avram F, Pistorius MR (2004) Russian and American put options under exponential phase-type Lévy models. Stochastic Processes Their Appl. 109(1):79–111.Crossref, Google Scholar
• [2] Avanzi B, Gerber HU, Shiu ES (2007) Optimal dividends in the dual model. Insurance Math. Econom. 41(1):111–123.Crossref, Google Scholar
• [3] Avram F, Palmowski Z, Pistorius MR (2007) On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Probab. 17(1):156–180.Crossref, Google Scholar
• [4] Baurdoux EJ, Yamazaki K (2015) Optimality of doubly reflected Lévy processes in singular control. Stochastic Processes Their Appl. 125(7):2727–2751.Crossref, Google Scholar
• [5] Bayraktar E, Egami M (2008) Optimizing venture capital investments in a jump diffusion model. Math. Methods Oper. Res. 67(1):21–42.Crossref, Google Scholar
• [6] Bayraktar E, Kyprianou AE, Yamazaki K (2013) On optimal dividends in the dual model. ASTIN Bull. 43(3):359–372.Crossref, Google Scholar
• [7] Beneš VE, Shepp LA, Witsenhausen HS (1980) Some solvable stochastic control problems. Stochastics 4(1):39–83.Crossref, Google Scholar
• [8] Benkherouf L, Bensoussan A (2009) Optimality of an (s,S) policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. SIAM J. Control Optim. 48(2):756–762.Crossref, Google Scholar
• [9] Bensoussan A, Liu R, Sethi SP (2005) Optimality of an (s,S) policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. SIAM J. Control Optim. 44(5):1650–1676.Crossref, Google Scholar
• [10] Bertoin J (1996) Lévy Processes (Cambridge University Press, Cambridge, UK).Google Scholar
• [11] Biffis E, Kyprianou AE (2010) A note on scale functions and the time value of ruin for Lévy insurance risk processes. Insurance Math. Econom. 46(1):85–91.Crossref, Google Scholar
• [12] Boetius F, Kohlmann M (1998) Connections between optimal stopping and singular stochastic control. Stochastic Process. Appl. 77(2):253–281.Crossref, Google Scholar
• [13] Cai N, Yang X (2018) International reserve management: A drift-switching reflected jump-diffusion model. Math. Finance 28(1):409–446.Crossref, Google Scholar
• [14] Carr P, Geman H, Madan DB, Yor M (2002) The fine structure of asset returns: An empirical investigation. J. Bus. 75(2):305–332.Crossref, Google Scholar
• [15] Guo X, Tomecek P (2008) Connections between singular control and optimal switching. SIAM J. Control Optim. 47(1):421–443.Crossref, Google Scholar
• [16] Guo X, Tomecek P (2009) A class of singular control problems and the smooth fit principle. SIAM J. Control Optim. 47(6):3076–3099.Crossref, Google Scholar
• [17] Hernández-Hernández D, Yamazaki K (2015) Games of singular control and stopping driven by spectrally one-sided Lévy processes. Stochastic Process. Appl. 125(1):1–38.Crossref, Google Scholar
• [18] Hernández-Hernández D, Perez JL, Yamazaki K (2016) Optimality of refraction strategies for spectrally negative Lévy processes. SIAM J. Control Optim. 54(3):1126–1156.Crossref, Google Scholar
• [19] Karatzas I, Shreve SE (1984) Connections between optimal stopping and singular stochastic control I. monotone follower problems. SIAM J. Control Optim. 22(6):856–877.Crossref, Google Scholar
• [20] Karatzas I, Shreve SE (1985) Connections between optimal stopping and singular stochastic control II. reflected follower problems. SIAM J. Control Optim. 23(3):433–451.Crossref, Google Scholar
• [21] Kuznetsov A, Kyprianou AE, Pardo JC (2012) Meromorphic Lévy processes and their fluctuation identities. Ann. Appl. Probab. 22(3):1101–1135.Crossref, Google Scholar
• [22] Kyprianou AE (2014) Fluctuations of Lévy Processes with Applications: Introductory Lectures (Springer, Berlin).Crossref, Google Scholar
• [23] Loeffen RL (2008) On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes. Ann. Appl. Probab. 18(5):1669–1680.Crossref, Google Scholar
• [24] Long M, Zhang H (2019) On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models. Stochastic Process. Appl. 129(8):2821–2849.Crossref, Google Scholar
• [25] Ma J (1992) On the principle of smooth fit for a class of singular stochastic control problems for diffusions. SIAM J. Control Optim. 30(4):975–999.Crossref, Google Scholar
• [26] Ma J (1993) Discontinuous reflection, and a class of singular stochastic control problems for diffusions. Stochastics 44(3-4):225–252.Google Scholar
• [27] Merhi A, Zervos M (2007) A model for reversible investment capacity expansion. SIAM J. Control Optim. 46(3):839–876.Crossref, Google Scholar
• [28] Mundaca G, Øksendal B (1998) Optimal stochastic intervention control with application to the exchange rate. J. Math. Econom. 2(29):225–243.Crossref, Google Scholar
• [29] Noba K (2021) On the optimality of double barrier strategies for Lévy processes. Stochastic Processes Their Appl. 131:73–102.Crossref, Google Scholar
• [30] Øksendal B, Sulem A (2012) Singular stochastic control and optimal stopping with partial information of Itô–Lévy processes. SIAM J. Control Optim. 50(4):2254–2287.Crossref, Google Scholar
• [31] Pérez JL, Yamazaki K, Bensoussan A (2020) Optimal periodic replenishment policies for spectrally positive Lévy demand processes. SIAM J. Control Optim. 58(6):3428–3456.Crossref, Google Scholar
• [32] Protter PE (2005) Stochastic differential equations. Stochastic Integration and Differential Equations (Springer, Berlin), 249–361.Crossref, Google Scholar
• [33] Surya BA (2007) An approach for solving perpetual optimal stopping problems driven by Lévy processes. Stochastics 79(3–4):337–361.Crossref, Google Scholar
• [34] Yamazaki K (2017) Inventory control for spectrally positive Lévy demand processes. Math. Oper. Res. 42(1):212–237.Link, Google Scholar