Article
Mathematics, Interdisciplinary Applications
Subrata Golui, Chandan Pal, Subhamay Saha
Summary: This paper explores two-person zero-sum stochastic games for controlled continuous time Markov decision processes with risk-sensitive discounted cost criterion, proving the existence of game value and saddle-point equilibrium under specific conditions, achieved through studying the corresponding Hamilton-Jacobi-Isaacs equation.
DYNAMIC GAMES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Subrata Golui, Chandan Pal
Summary: This paper considers the zero-sum stochastic games for controlled continuous time Markov processes on a general state space with risk-sensitive discounted cost criteria. The transition and cost rates may be unbounded. Under a stability assumption, the existence of a saddle-point equilibrium in the class of Markov strategies is proven, and a characterization in terms of the corresponding Hamilton-Jacobi-Isaacs (HJI) equation is given. Additionally, the results and assumptions are illustrated through an example.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Mrinal K. Ghosh, Subrata Golui, Chandan Pal, Somnathi Pradhan
Summary: This paper investigates zero-sum stochastic games in continuous time with controlled Markov chains and with risk-sensitive average cost criterion. In this type of game, the transition and cost rates may be unbounded. We prove the existence of the game value and a saddle-point equilibrium among all stationary strategies under a Lyapunov stability condition. To achieve this, we establish the existence of a principal eigenpair for the corresponding Hamilton-Jacobi-Isaacs (HJI) equation, which is done using a nonlinear version of the Krein-Rutman theorem. We then characterize the saddle-point equilibrium in terms of the corresponding HJI equation. Finally, we provide an illustration of our results using a controlled population system.
MATHEMATICAL CONTROL AND RELATED FIELDS
(2023)
Article
Operations Research & Management Science
Yonghui Huang, Zhaotong Lian, Xianping Guo
Summary: This paper explores risk-sensitive piecewise deterministic Markov decision processes, focusing on minimizing the expected exponential utility of an infinite-horizon discounted cost. By introducing an auxiliary function with time as an additional variable, the problem is analyzed and optimal policies depending on time are shown to exist, highlighting the non-stationarity of risk-sensitive discounted optimal policies.
OPERATIONAL RESEARCH
(2022)
Article
Mathematics, Applied
Subrata Golui, Chandan Pal
Summary: This paper studies two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion, proving the existence of the game value and a Markov saddle-point equilibrium under suitable conditions in the class of all history-dependent multi-strategies by studying the corresponding risk-sensitive finite-horizon optimality equations.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2022)
Article
Operations Research & Management Science
Yonghui Huang, Zhaotong Lian, Xianping Guo
Summary: This paper investigates zero-sum piecewise deterministic Markov games with Borel state and action spaces, considering the expected infinite-horizon discounted payoff criterion. Both the transition rate and payoff rate can be unbounded. The players' policies are history-dependent, and the controls continuously act on the transition rate and the payoff rate. The paper develops Dynkin's formula and the comparison theorem, and shows that the game has a unique solution to the associated Shapley equation. A potential algorithm for computing saddle points is proposed based on a simple form of the Shapley equation.
MATHEMATICAL METHODS OF OPERATIONS RESEARCH
(2023)
Article
Mathematics
Martin Schechter
Summary: Solving Euler-Lagrange equations involves finding critical points of functionals, often done through the method of linking appropriate sets that separate the functional. The challenge lies in determining if the sets link, which requires adjustments to definitions for infinite dimensions and topology of the space. This adjustment allows for solutions in infinite dimensional splitting, replacing the usual Brouwer index with the Leray-Schauder index for proving theorems.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Interdisciplinary Applications
Chandan Pal, Somnath Pradhan
Summary: This paper studies zero-sum stochastic games for pure jump processes on a general state space with risk sensitive discounted criteria, and establishes a saddle point equilibrium in Markov strategies for bounded cost function by studying relevant Hamilton-Jacobi-Isaacs equations.
JOURNAL OF DYNAMICS AND GAMES
(2022)
Article
Mathematics, Applied
Mingshang Hu, Yifan Sun, Falei Wang
Summary: This paper examines backward stochastic differential equations (BSDEs) on the infinite horizon under consistent nonlinear expectations dominated by consistent sublinear expectations. The existence and uniqueness result is derived through discretization and approximation methods. Additionally, the existence of solutions for Markovian ergodic BSDEs under (G) over tilde -expectations is demonstrated, along with some applications mentioned.
BULLETIN DES SCIENCES MATHEMATIQUES
(2022)
Article
Operations Research & Management Science
Qingda Wei, Xian Chen
Summary: This paper studies discrete-time nonzero-sum stochastic games under the risk-sensitive first passage discounted cost criterion. The main results include the existence and uniqueness of the risk-sensitive first passage discounted optimal value function for each player, and the existence of a randomized Markov Nash equilibrium.
Article
Mathematics, Applied
Grzegorz Graff, Rafael Ortega, Alfonso Ruiz-Herrera
Summary: This study considers a class of dissipative orientation-preserving homeomorphisms of the infinite annulus, pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere. It is proven that, in some isotopy classes, the local behavior of such homeomorphisms at a fixed point, namely the existence of inverse saddle, impacts the topology of the attractor - it cannot be connected by an arc.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Mathematics, Applied
Martin Schechter
Summary: Results obtained for Landesman-Lazer type problems can be extended to operators with unbounded essential spectra, as long as they have an isolated eigenvalue of finite multiplicity.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Business, Finance
Martin Herdegen, David Hobson, Joseph Jerome
Summary: This study aims to provide a detailed introduction to infinite-horizon investment-consumption problems for agents with preferences described by Epstein-Zin (EZ) stochastic differential utility (SDU). By considering a novel description of EZ SDU in a Black-Scholes-Merton market, the necessity for the coefficients of relative risk aversion and of elasticity of intertemporal complementarity to lie on the same side is highlighted.
FINANCE AND STOCHASTICS
(2022)
Article
Automation & Control Systems
Zhifu Jia, Xinsheng Liu
Summary: This paper investigates the multifactor uncertain optimal control system with jumps, and proposes relevant models and methods, providing a new approach to solve the optimal strategy problem in dynamical systems.
INTERNATIONAL JOURNAL OF CONTROL
(2023)
Article
Mathematics, Applied
Arnab Bhabak, Subhamay Saha
Summary: This article examines zero-sum and non-zero sum risk-sensitive average criterion games for semi-Markov processes with a finite state space. For the zero-sum case, the article proves the existence of a value under certain assumptions and establishes the existence of a stationary saddle point equilibrium. For the non-zero sum case, the article proves the existence of a stationary Nash equilibrium under suitable assumptions.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
K. Suresh Kumar, Chandan Pal
STOCHASTIC ANALYSIS AND APPLICATIONS
(2015)
Article
Mathematics, Applied
K. Suresh Kumar, Chandan Pal
APPLIED MATHEMATICS AND OPTIMIZATION
(2013)
Review
Mathematics, Applied
Chandan Pal, Somnath Pradhan
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
(2019)
Article
Mathematics, Applied
Mrinal K. Ghosh, K. Suresh Kumar, Chandan Pal, Somnath Pradhan
Summary: In this study, nonzero-sum stochastic differential games with risk-sensitive discounted cost criteria were examined. A Nash equilibrium in Markov strategies for the discounted cost criterion was established under fairly general conditions on drift term and diffusion coefficients. The results were achieved through studying relevant systems of coupled HJB equations.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Subrata Golui, Chandan Pal
Summary: This paper studies two-person zero-sum stochastic games for controlled continuous time Markov chains with risk-sensitive finite-horizon cost criterion, proving the existence of the game value and a Markov saddle-point equilibrium under suitable conditions in the class of all history-dependent multi-strategies by studying the corresponding risk-sensitive finite-horizon optimality equations.
STOCHASTIC ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Arnab Bhabak, Chandan Pal, Subhamay Saha
Summary: "This paper studies a semi-Markov zero-sum stochastic game with a general state and finite action spaces, analyzing performance through a probability criterion. The existence of the game's value is established under suitable assumptions and characterized through an optimality equation, with a prescribed saddle point equilibrium also provided."
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
(2022)
Article
Mathematics, Interdisciplinary Applications
Subrata Golui, Chandan Pal, Subhamay Saha
Summary: This paper explores two-person zero-sum stochastic games for controlled continuous time Markov decision processes with risk-sensitive discounted cost criterion, proving the existence of game value and saddle-point equilibrium under specific conditions, achieved through studying the corresponding Hamilton-Jacobi-Isaacs equation.
DYNAMIC GAMES AND APPLICATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Chandan Pal, Somnath Pradhan
Summary: This paper studies zero-sum stochastic games for pure jump processes on a general state space with risk sensitive discounted criteria, and establishes a saddle point equilibrium in Markov strategies for bounded cost function by studying relevant Hamilton-Jacobi-Isaacs equations.
JOURNAL OF DYNAMICS AND GAMES
(2022)
Article
Operations Research & Management Science
Subrata Golui, Chandan Pal
Summary: This paper investigates the risk-sensitive discounted control problem for continuous-time jump Markov processes. The transition rates and cost rates of the underlying processes are allowed to be unbounded. Under certain conditions, the existence and uniqueness of the solution to the Hamilton-Jacobi-Bellman equation are established. Moreover, the existence of optimal risk-sensitive control in the class of Markov control is proved and the optimal control is completely characterized.
MATHEMATICAL METHODS OF OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
Mrinal K. Ghosh, Subrata Golui, Chandan Pal, Somnath Pradhan
Summary: We study the nonzero-sum stochastic games for continuous time Markov decision processes on a denumerable state space with risk-sensitive ergodic cost criterion. Under a Lyapunov type stability assumption, we show the existence of a Nash equilibrium in stationary strategies by proving the solvability of the corresponding system of coupled HJB equations. Utilizing principal eigenvalues associated with the HJB equations, we completely characterize the Nash equilibria in the space of stationary Markov strategies.
APPLIED MATHEMATICS AND OPTIMIZATION
(2022)
Article
Operations Research & Management Science
Chandan Pal, Subhamay Saha
OPERATIONS RESEARCH LETTERS
(2020)
Article
Multidisciplinary Sciences
K. Suresh Kumar, Chandan Pal
