Papers by Davide De Santis
The thesis explores general stochastic differential games involving impulse controls and ultimate... more The thesis explores general stochastic differential games involving impulse controls and ultimately investigates competition in dealer markets. The work begins with the first chapter on general non-zero stochastic differential games between an impulse controller and a stopper, providing the first model of such class of games using impulse controls. Nash equilibria are characterised through a verification theorem, which identifies a new system of quasi-variational inequalities whose solution gives equilibrium payoffs with the correspondent strategies. Then, in order to show how the verification theorem is meant to be applied, an example is shown and two different types of Nash equilibrium are fully characterised. To conclude, some numerical results describing the qualitative properties of both types of equilibrium are provided. The dissertation continues with the second chapter on general zero-sum stochastic differential games with impulse controls. Here, two agents play feedback imp...
We study a two-player nonzero-sum stochastic differential game where one player controls the stat... more We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash equilibria through a verification theorem, which identifies a new system of quasi-variational inequalities whose solution gives equilibrium payoffs with the correspondent strategies. Moreover, we apply the verification theorem to a game with a one-dimensional state variable, evolving as a scaled Brownian motion, and with linear payoff and costs for both players. Two types of Nash equilibrium are fully characterized, i.e. semi-explicit expressions for the equilibrium strategies and associated payoffs are provided. Both equilibria are of threshold type: in one equilibrium players' intervention are not simultaneous, while in the other one the first player induces her competitor to stop the game. Finally, we provide some numerical results describing the q...
Journal of Optimization Theory and Applications
We study a two-player nonzero-sum stochastic differential game, where one player controls the sta... more We study a two-player nonzero-sum stochastic differential game, where one player controls the state variable via additive impulses, while the other player can stop the game at any time. The main goal of this work is to characterize Nash equilibria through a verification theorem, which identifies a new system of quasivariational inequalities, whose solution gives equilibrium payoffs with the correspondent strategies. Moreover, we apply the verification theorem to a game with a one-dimensional state variable, evolving as a scaled Brownian motion, and with linear payoff and costs for both players. Two types of Nash equilibrium are fully characterized, i.e. semi-explicit expressions for the equilibrium strategies and associated payoffs are provided. Both equilibria are of threshold type: in one equilibrium players’ intervention are not simultaneous, while in the other one the first player induces her competitor to stop the game. Finally, we provide some numerical results describing the ...
Uploads
Papers by Davide De Santis