Finite-Time Horizon, Stopper vs. Singular-Controller Games on the Half-Line
Published Online:2 Jan 2026https://doi.org/10.1287/moor.2024.0690
References
- [1] (2017) Stochastic Calculus, Universitext (Springer, Cham, Switzerland).Crossref, Google Scholar
- [2] (2013) On the multidimensional controller-and-stopper games. SIAM J. Control Optim. 51(2):1263–1297.Crossref, Google Scholar
- [3] (2011) Proving regularity of the minimal probability of ruin via a game of stopping and control. Finance Stochastics 15(4):785–818.Crossref, Google Scholar
- [4] (1974) Nonlinear variational inequalities and differential games with stopping times. J. Functional Anal. 16(3):305–352.Crossref, Google Scholar
- [5] (1982) Applications of Variational Inequalities in Stochastic Control, Studies in Mathematics and its Applications, vol. 12 (North-Holland Publishing Co., Amsterdam).Google Scholar
- [6] (2008) Optimal investment decisions when time-horizon is uncertain. J. Math. Econom. 44(11):1100–1113.Crossref, Google Scholar
- [7] (2025) On the saddle point of a zero-sum stopper vs. singular-controller game. Stochastic Processes Appl. 182:104555.Crossref, Google Scholar
- [8] (2025a) Variational inequalities on unbounded domains for zero-sum singular-controller vs. stopper games. Math. Oper. Res. 50(1):277–312.Link, Google Scholar
- [9] (2024) Zero-sum stopper vs. singular-controller games with constrained control directions. SIAM J. Control Optim. 62(4):2203–2228.Crossref, Google Scholar
- [10] (2025b) Stopper vs. singular-controller games with degenerate diffusions. Appl. Math. Optim. 91:3.Crossref, Google Scholar
- [11] (1951) On a quasi-linear parabolic equation occurring in aerodynamics. Quart. Appl. Math. 9(3):225–236.Crossref, Google Scholar
- [12] (1994) A problem of singular stochastic control with discretionary stopping. Ann. Appl. Probab. 4(1):226–240.Crossref, Google Scholar
- [13] (2017) The dividend problem with a finite horizon. Ann. Appl. Probab. 27(6):3525–3546.Crossref, Google Scholar
- [14] (2022) A numerical scheme for stochastic differential equations with distributional drift. Stochastic Processes Appl. 154:55–90.Crossref, Google Scholar
- [15] (1979) A second order elliptic equation with gradient constraint. Comm. Partial Differential Equations 4(5):555–572.Crossref, Google Scholar
- [16] (2020) On the singular control of exchange rates. Ann. Oper. Res. 292(2):795–832.Crossref, Google Scholar
- [17] (1975) Deterministic and Stochastic Optimal Control, Applications of Mathematics, vol. 1 (Springer, New York).Crossref, Google Scholar
- [18] (2006) Controlled Markov Processes and Viscosity Solutions, Stochastic Modelling and Applied Probability, vol. 25, 2nd ed. (Springer, New York).Google Scholar
- [19] (1973) Stochastic games and variational inequalities. Archive Rational Mech. Anal. 51(5):321–346.Crossref, Google Scholar
- [20] (2008) Partial Differential Equations of Parabolic Type (Dover Publications, Mineola, NY).Google Scholar
- [21] (2013) Optimal consumption in a Brownian model with absorption and finite time horizon. Appl. Math. Optim. 67:197–241.Crossref, Google Scholar
- [22] (2014) Existence and asymptotic behavior of an optimal barrier for an optimal consumption problem in a Brownian model with absorption and finite time horizon. Appl. Math. Optim. 69:233–271.Crossref, Google Scholar
- [23] (2015) An optimal consumption problem in finite time with a constraint on the ruin probability. Finance Stochastics 19(4):791–847.Crossref, Google Scholar
- [24] (2006) Mixed zero-sum stochastic differential game and American game options. SIAM J. Control Optim. 45(2):496–518.Crossref, Google Scholar
- [25] (2015) A zero-sum game between a singular stochastic controller and a discretionary stopper. Ann. Appl. Probab. 25(1):46–80.Crossref, Google Scholar
- [26] (2024) Callable convertible bonds under liquidity constraints and hybrid priorities. SIAM J. Financial Math. 15(4):1083–1123.Crossref, Google Scholar
- [27] (1950) The partial differential equation ut+uux=μxx. Comm. Pure Appl. Math. 3(3):201–230.Crossref, Google Scholar
- [28] (2013) Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control. ESAIM: COCV 19(1):112–128.Crossref, Google Scholar
- [29] (1983) Boundary regularity and uniqueness for an elliptic equations with gradient constraint. Comm. Partial Differential Equations 8(4):317–346.Crossref, Google Scholar
- [30] (2008) Martingale approach to stochastic differential games of control and stopping. Ann. Probab. 36(4):1495–1527.Crossref, Google Scholar
- [31] (2019) HJB equations with gradient constraint associated with controlled jump-diffusion processes. SIAM J. Control Optim. 57(3):2185–2213.Crossref, Google Scholar
- [32] (2000) Game options. Finance Stochastics 4:443–463.Crossref, Google Scholar
- [33] (2013) Dynkin’s games and Israeli options. Internat. Scholarly Res. Notices 2013(1):856458.Google Scholar
- [34] (2024) Mortgage contracts and underwater default. SIAM J. Financial Math. 15(2):315–359.Crossref, Google Scholar
- [35] (2009) Controlled Diffusion Processes, Stochastic Modelling and Applied Probability, vol. 14 (Springer, Berlin). [Translated from the 1977 Russian original by A.B. Aries, reprint of the 1980 edition.]Google Scholar
- [36] (2004) Some calculations for Israeli options. Finance Stochastics 8:73–86.Crossref, Google Scholar
- [37] (1996) Optimal target zones: How an exchange rate mechanism can improve upon discretion. J. Econom. Dynamic Control 20(9–10):1641–1660.Crossref, Google Scholar
- [38] (2015) Optimal stopping under adverse nonlinear expectation and related games. Ann. Appl. Probab. 25(5):2503–2534.Crossref, Google Scholar
- [39] (2005) Stochastic Integration and Differential Equations, Stochastic Modelling and Applied Probability, vol. 21, 2nd ed. (Springer, Berlin).Crossref, Google Scholar
- [40] (2009) Optimal stopping with multiple priors. Econometrica 77(3):857–908.Crossref, Google Scholar
- [41] (2006) A two-person game for pricing convertible bonds. SIAM J. Control Optim. 45(4):1508–1539.Crossref, Google Scholar
- [42] (2004) Perpetual convertible bonds. SIAM J. Control Optim. 43(1):58–85.Crossref, Google Scholar
- [43] (1981) The C1,1–character of solutions of second order elliptic equations with gradient constraint. Comm. Partial Differential Equations 6(3):361–371.Crossref, Google Scholar
- [44] (2014) Game call options revisited. Math. Finance 24(1):173–206.Crossref, Google Scholar
- [45] (2004) Optimal investment strategy to minimize the probability of lifetime ruin. North Amer. Actuarial J. 8(4):106–126.Crossref, Google Scholar

