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We study the problem of asset liquidation in financial systems. During financial crises, asset liquidation is often inevitable but can lead to substantial losses if a significant amount of illiquid assets are sold simultaneously at…

In this paper, we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model. Investment in the foreign market is allowed, and therefore, the foreign…

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…

In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…

We consider financial networks, where banks are connected by contracts such as debts or credit default swaps. We study the clearing problem in these systems: we want to know which banks end up in a default, and what portion of their…

We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external…

A problem of optimal debt management is modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process.…

The current global financial system forms a highly interconnected network where a default in one of its nodes can propagate to many other nodes, causing a catastrophic avalanche effect. In this paper we consider the problem of reducing the…

We study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout…

This paper considers the problem faced by a bank which trades in the funds market so as to maintain the reserve requirements and minimize the costs of doing that. We work in a stochastic paradigm and the reserve requirements are determined…

We prove the global-time existence of weak solutions to the supercooled Stefan problem. Our result holds in general space dimensions and with a general class of initial data. In addition, our solution is maximal in the sense of a certain…

The model of this paper gives a convenient strategy that a bank in the federal funds market can use in order to maximize its profit in a contemporaneous reserve requirement (CRR) regime. The reserve requirements are determined by the demand…

We consider the problem of governing systemic risk in a banking system model. The banking system model consists in an initial value problem for a system of stochastic differential equations whose dependent variables are the log-monetary…

We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…

We investigate the existence of an optimal policy to monitor a mean field systems of agents managing a risky project under moral hazard with accidents modeled by L\'evy processes magnified by the law of the project. We provide a general…

Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads…

The process of contagiousness spread modelling is well-known in epidemiology. However, the application of spread modelling to banking market is quite recent. In this work, we present a system of ordinary differential equations, simulating…

We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a…

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that…