2014/08/16 by Bayraktar, Erhan, Zhou, Zhou
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR)
paper · doi:10.48550/arxiv.1408.3692
On a filtered probability space (Ω,F,P,\mathbbF=(Ft)t=0,\dotso,T), we consider stopper-stopper games V:=inf\Rho∈\bTiisupτ∈\T\E[U(\Rho(τ),τ)] and \underline V:=sup\Tau∈\bTiinfρ∈\T\E[U(\Rho(τ),τ)] in discrete time, where U(s,t) is Fs\vee t-measurable instead of Fs\wedge t-measurable as is often assumed in the literature, \T is the set of stopping times, and \bTi and \bTii are sets of mappings from \T to \T satisfying certain non-anticipativity conditions. We convert the problems into a corresponding Dynkin game, and show that V=\underline V=V, where V is the value of the Dynkin game. We also get the optimal \Rho∈\bTii and \Tau∈\bTi for V and \underline V respectively.