Arbeitspapier

Linear-quadratic-singular stochastic differential games and applications

to related objects

We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.

Language: Englisch

Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 678

Classification: Mathematik

Subject: Singular stochastic control
linear quadratic games
stochastic maximum principle
Nash equilibrium

Event: Geistige Schöpfung

(who): Dianetti, Jodi

Event: Veröffentlichung

(who): Bielefeld University, Center for Mathematical Economics (IMW)

(where): Bielefeld

(when): 2023

Handle: http://hdl.handle.net/10419/278468

URN: urn:nbn:de:0070-pub-29786777

Last update: 10.03.2025, 11:42 AM CET

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Object type

Arbeitspapier

Associated

Dianetti, Jodi
Bielefeld University, Center for Mathematical Economics (IMW)

Time of origin

2023

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