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I. Karatzas, I. Zamfirescu (2005)
Game approach to the optimal stopping problem†Stochastics, 77
R. Korn (1999)
Some applications of impulse control in mathematical financeMathematical Methods of Operations Research, 50
Jakša Cvitanić, I. Karatzas (1996)
Backward stochastic differential equations with reflection and Dynkin gamesAnnals of Probability, 24
R. Aïd, Matteo Basei, Giorgia Callegaro, L. Campi, Tiziano Vargiolu (2016)
Nonzero-Sum Stochastic Differential Games with Impulse Controls: A Verification Theorem with ApplicationsMath. Oper. Res., 45
B. Bouchard, N. Touzi (2011)
Weak Dynamic Programming Principle for Viscosity SolutionsSIAM J. Control. Optim., 49
Alexander Triantis, James Hodder (1990)
Valuing Flexibility as a Complex OptionJournal of Finance, 45
Patrick Jaillet, Ehud Ronn, S. Tompaidis (2004)
Valuation of Commodity-Based Swing OptionsManag. Sci., 50
M. Jeanblanc-Picqué (1993)
Impulse Control Method and Exchange RateMathematical Finance, 3
(1992)
Ishii
J. Yong (1994)
Zero-sum differential games involving impulse controlsApplied Mathematics and Optimization, 29
Idris Kharroubi, Jin Ma, H. Pham, Jianfeng Zhang (2008)
Backward SDEs with constrained jumps and quasi-variational inequalitiesAnnals of Probability, 38
Ł. Stettner (1982)
Zero-sum Markov games with stopping and impulsive strategiesApplied Mathematics and Optimization, 9
Parsiad Azimzadeh (2016)
A Zero-Sum Stochastic Differential Game with Impulses, Precommitment, and Unrestricted Cost FunctionsApplied Mathematics & Optimization, 79
M. Crandall, H. Ishii, P. Lions (1992)
User’s guide to viscosity solutions of second order partial differential equationsBulletin of the American Mathematical Society, 27
Joseph Lewin (1994)
Differential Games
A. Cadenillas, F. Zapatero (1999)
Optimal Central Bank Intervention in the Foreign Exchange MarketJournal of Economic Theory, 87
Yanni Chen, Xin Guo (2011)
Impulse Control of Multidimensional Jump Diffusions in Finite Time HorizonSIAM J. Control. Optim., 51
M. Jeanblanc-Picqué, A. Shiryaev (1995)
Optimization of the flow of dividendsRussian Mathematical Surveys, 50
Andrea Cosso (2012)
Stochastic Differential Games Involving Impulse Controls and Double-Obstacle Quasi-variational InequalitiesSIAM J. Control. Optim., 51
Shanjian Tang, J. Yong (1993)
Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approachStochastics and Stochastics Reports, 45
L. Evans, P. Souganidis (1983)
Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations.Indiana University Mathematics Journal, 33
(2007)
Introduction to stochastic control of mixed diffusion processes, viscosity solutions and applications in finance and insurance
Huy Pham (1998)
Optimal Stopping of Controlled Jump Diiusion Processes: a Viscosity Solution Approach
Erhan Bayraktar, Yu‐Jui Huang (2010)
On the Multi-Dimensional Controller-and-Stopper GamesERN: Other Game Theory & Bargaining Theory (Topic)
S. Hamadène, M. Hassani (2005)
BSDEs with two reflecting barriers : the general resultProbability Theory and Related Fields, 132
(1989)
On the existence of value functions of two-player
Vathana Vath, M. Mnif, H. Pham (2006)
A model of optimal portfolio selection under liquidity risk and price impactFinance and Stochastics, 11
Feng Zhang (2011)
Stochastic differential games involving impulse controlsESAIM: Control, Optimisation and Calculus of Variations, 17
R. Korn (1998)
Portfolio optimisation with strictly positive transaction costs and impulse controlFinance and Stochastics, 2
F. Benth, V. Kholodnyi, P. Laurence (2014)
Quantitative energy finance
J. Eastham, Kevin Hastings (1988)
Optimal Impulse Control of PortfoliosMath. Oper. Res., 13
Naïma El Farouq, G. Barles, P. Bernhard (2010)
Deterministic Minimax Impulse ControlApplied Mathematics and Optimization, 61
A. Cadenillas, Tahir Choulli, M. Taksar, Lei Zhang (2006)
CLASSICAL AND IMPULSE STOCHASTIC CONTROL FOR THE OPTIMIZATION OF THE DIVIDEND AND RISK POLICIES OF AN INSURANCE FIRMMathematical Finance, 16
G. Mundaca, B. Øksendal, B. Øksendal (1998)
Optimal stochastic intervention control with application to the exchange rateJournal of Mathematical Economics, 29
B. Asri (2013)
Minimax Impulse Control Problems in Finite HorizonarXiv: Optimization and Control
B. Asri (2011)
Stochastic Optimal Multi-Modes Switching with a Viscosity Solution ApproachArXiv, abs/1102.1256
Erhan Bayraktar, Thomas Emmerling, J. Menaldi (2012)
On the Impulse Control of Jump DiffusionsEconometrics: Mathematical Methods & Programming eJournal
A. Morton, S. Pliska (1995)
OPTIMAL PORTFOLIO MANAGEMENT WITH FIXED TRANSACTION COSTSMathematical Finance, 5
S. Vajda, R. Isaacs (1967)
Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and OptimizationThe Mathematical Gazette, 51
D. Mauer, Alexander Triantis (1994)
Interactions of Corporate Financing and Investment Decisions: A Dynamic FrameworkJournal of Finance, 49
R. Isaacs (1999)
Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization
R. Seydel (2009)
Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusionsStochastic Processes and their Applications, 119
B. Asri (2010)
Deterministic minimax impulse control in finite horizon: the viscosity solution approachESAIM: Control, Optimisation and Calculus of Variations, 19
B. Øksendal, A. Sulem (2001)
Optimal Consumption and Portfolio with Both Fixed and Proportional Transaction CostsSIAM J. Control. Optim., 40
I. Karatzas, Hui Wang (2000)
A Barrier Option of American TypeApplied Mathematics and Optimization, 42
R. Buckdahn, Juan Li (2007)
Stochastic Differential Games and Viscosity Solutions of Hamilton--Jacobi--Bellman--Isaacs EquationsSIAM J. Control. Optim., 47
Christoph Belak, S. Christensen, F. Seifried (2017)
A General Verification Result for Stochastic Impulse Control ProblemsSIAM J. Control. Optim., 55
(1966)
Topolgy
G. Beer (1993)
Topologies on Closed and Closed Convex Sets
WH Fleming, PE Souganidis (1989)
On the existence of value functions of two-player, zero-sum stochastic differential gamesIndiana Univ. Math. J., 38
This paper considers the problem of two-player zero-sum stochastic differential game with both players adopting impulse controls in finite horizon under rather weak assumptions on the cost functions (c and χ not decreasing in time). We use the dynamic programming principle and viscosity solutions approach to show existence and uniqueness of a solution for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) partial differential equation (PDE) of the game. We prove that the upper and lower value functions coincide. Keywords Stochastic differential game · Impulse control · Quasi-variational inequality · Viscosity solution Mathematics Subject Classification 93E20 · 49L20 · 49L25 · 49N70 1 Introduction The theory of differential games with Elliot–Kalton strategies in the viscosity solution framework was initiated by Evans and Souganidis [21]. Fleming and Souganidis [22] studied in a rigorous manner two-player zero-sum stochastic differential games and their work translated former results on differential games from the purely deterministic into the stochastic framework. Subsequently, Buckdahn and Li [10] generalized the framework introduced in [22]. In this paper, we consider the state process of the stochastic differential game, defined as the solution of the following stochastic equation: B Brahim El Asri b.elasri@uiz.ac.ma Sehail Mazid sehail.mazid@edu.uiz.ac.ma Université Ibn Zohr, Equipe, Aide á la decision,
Applied Mathematics and Optimization – Springer Journals
Published: Sep 24, 2018
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