Defines responsive distributions for G-normal random variables and proposes a convergent coupled trinomial tree algorithm to compute G-expectations and sample the induced laws.
Nonlinear Expectations and Stochastic Calculus under Uncertainty
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abstract
In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under sublinear expectation. We also present a new type of Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide robust tools for the problem of probability model uncertainty arising from financial risk management, statistics and stochastic controls.
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The paper establishes existence and uniqueness for non-Lipschitz G-BSDEs under uniform continuity and monotonicity, then derives the dynamic programming principle and HJB viscosity solution connection for the corresponding stochastic recursive optimal control problem.
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Responsive Distribution of G-normal Random Variables
Defines responsive distributions for G-normal random variables and proposes a convergent coupled trinomial tree algorithm to compute G-expectations and sample the induced laws.