Stability for gains from large investors' strategies in M1/J1 topologies

One crucial aspect for market impact models is the definition of gains from block trade: the large investor should be unable to circumvent liquidity cost by fast trading in small blocks or rates. Skorokhod's J1 topology... [ view full abstract ]

One crucial aspect for market impact models is the definition of gains from block trade: the large investor should be unable to circumvent liquidity cost by fast trading in small blocks or rates. Skorokhod's J₁ topology cannot cover such approximations of a trading strategy; unlike Skorokhod's M₁ topology. Starting from a general model for observed price being a function of an unperturbed price and controlled impact, we extend the gains functional from continuous finite-variation to adapted càdlàg strategies, continuously in M₁ in probability. A large class of strategies helps with optimal liquidation problems, and is a prerequisite for e.g. hedging.