In this short note we consider reflected backward stochastic differential equations(RBSDEs)with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous.In this case,the barrier is rep...In this short note we consider reflected backward stochastic differential equations(RBSDEs)with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous.In this case,the barrier is represented as a nondecreasing limit of right continuous with left limit(RCLL)barriers.We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions.Finally,we highlight the connection of these RBSDEs with standard RCLL BSDEs.展开更多
In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We ai...In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We aim to elucidate various properties of the value function family within this context.We prove the existence of an optimal predictable stopping time,subject to specific assumptions regarding the reward functionϕ.展开更多
We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This settin...We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This setting is more general than PEP TESU the classical setup of stochastic processes,notably allowing for general payoff processes that are not necessarily right-continuous.Under weaker integrability,with regularity assumptions for the reward family Y=(Y(u),u E S),the existence of an optimal stopping time is demonstrated.Sufficient conditions for the existence of an optimal model are then determined.For this purpose,we present a universal optional decomposition for the generalized Snell envelope family associated with Y.This decomposition is then employed to prove the existence of an optimal probability model and to study its properties.展开更多
文摘In this short note we consider reflected backward stochastic differential equations(RBSDEs)with a Lipschitz driver and barrier processes that are optional and right lower semicontinuous.In this case,the barrier is represented as a nondecreasing limit of right continuous with left limit(RCLL)barriers.We combine some well-known existence results for RCLL barriers with comparison arguments for the control process to construct solutions.Finally,we highlight the connection of these RBSDEs with standard RCLL BSDEs.
文摘In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We aim to elucidate various properties of the value function family within this context.We prove the existence of an optimal predictable stopping time,subject to specific assumptions regarding the reward functionϕ.
文摘We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This setting is more general than PEP TESU the classical setup of stochastic processes,notably allowing for general payoff processes that are not necessarily right-continuous.Under weaker integrability,with regularity assumptions for the reward family Y=(Y(u),u E S),the existence of an optimal stopping time is demonstrated.Sufficient conditions for the existence of an optimal model are then determined.For this purpose,we present a universal optional decomposition for the generalized Snell envelope family associated with Y.This decomposition is then employed to prove the existence of an optimal probability model and to study its properties.
