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5 papers · 2 filters
Lyapunov-type conditions and stochastic differential equations driven by -Brownian motion
Xinpeng Li, Xiangyun Lin, Yiqing Lin
This paper studies the solvability and the stability of stochastic differential equations driven by G-Brownian motion (GSDEs). In particular, the existence and uniqueness of the so…
Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs
Zhenjie Ren, Nizar Touzi, Jianfeng Zhang
This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduc…
Fixation results for the two-feature Axelrod model with a variable number of opinions
Nicolas Lanchier, Paul-Henri Moisson
The Axelrod model is a spatial stochastic model for the dynamics of cultures that includes two key social mechanisms: homophily and social influence, respectively defined as the te…
Almost sure optimal hedging strategy
Emmanuel Gobet, Nicolas Landon
In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional Itô model when the discrete rebalancing d…
On small-noise equations with degenerate limiting system arising from volatility models
Giovanni Conforti, Stefano De Marco, Jean-Dominique Deuschel
The one-dimensional SDE with non Lipschitz diffusion coefficient is widely studied in mathematical finance. Several works…