RBDSDEs with jumps and optional Barrier and mean field game with common noise

• In this paper, we study a generalization of reflected backward doubly stochastic differential equations (RBDSDEs) and present a link to a general mean field game. In our case, the RBDSDEs are associated with a lower optional not right continuous barrier. First, we establish the existence and uniqueness of a solution of such RBDSDEs. We then study a mean field game with a new type of common noise related to an electricity grid with storage allowing jumps and prove the existence of a mean field Nash equilibrium.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Reflected backward doubly stochastic differential equations

mertens decomposition

strong optional supermartingale

mean field game

common noise mean field nash equilibrium

Mathematics

Matematik

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