Generators of measure-valued jump-diffusions

Measure-valued jump-diffusions provide useful approximations of large stochastic systems in finance, such as large sets of equity returns, limit order books, and particle systems with mean-field interaction. The dynamics of a... [ view full abstract ]

Measure-valued jump-diffusions provide useful approximations of large stochastic systems in finance, such as large sets of equity returns, limit order books, and particle systems with mean-field interaction. The dynamics of a measure-valued jump-diffusion is governed by an integro-differential operator of Levy type, expressed using a notion of derivative that is well-known from the superprocess literature, but different from the Lions derivative frequently used in the context of mean-field games. General and easy-to-use existence criteria for jump-diffusions valued in probability measures are derived using new optimality conditions for functions of measure arguments. Further applications include optimal control of measure-valued state processes.