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One-dimensional reflected bsdes with two barriers under logarithmic growth and applications

El Asri Brahim, Oufdil Khalid, Ourkiya Nacer

Probability and Mathematical Statistics

2022

Vol. 42, Fasc. 2

251--282

We deal with the problem of existence and uniqueness of a solution for one-dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator has logarithmic growth |y| |ln |y|| + |z|√(|ln |z||) in the state variables y and z. The terminal value ξ and the obstacle processes (Lt)0≤t≤T and (Ut)0≤t≤T are Lp-integrable for a suitable p > 2. The main idea is to use the concept of local solution to construct a global one. As applications, we broaden the class of functions for which mixed zero-sum stochastic differential games admit an optimal strategy and the related double-obstacle partial differential equation problem has a unique viscosity solution.