• Corpus ID: 240419862

Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

@inproceedings{Cuchiero2021OptimalBS,
  title={Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem},
  author={Christa Cuchiero and Christoph Reisinger and Stefan Rigger},
  year={2021}
}
We consider the problem faced by a central bank which bails out distressed financial institutions that pose systemic risk to the banking sector. In a structural default model with mutual obligations, the central agent seeks to inject a minimum amount of cash in order to limit defaults to a given proportion of entities. We prove that the value of the central agent’s control problem converges as the number of defaultable institutions goes to infinity, and that it satisfies a drift controlled… 
1 Citations
Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups
We consider two approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a

References

SHOWING 1-10 OF 54 REFERENCES
Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance
Many nonlinear option pricing problems can be formulated as optimal control problems, leading to Hamilton-Jacobi-Bellman (HJB) or Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations. We show that such
Numerical valuation of basket credit derivatives in structural jump-diffusion models
We consider a model where each company’s asset value follows a jump-diusion process, and is connected with other companies via global factors. Motivated by ideas in Bush et al. (2011), where the
Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications
We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weighting matrices in the cost
Bellman equation and viscosity solutions for mean-field stochastic control problem
We consider the stochastic optimal control problem of McKean-Vlasov stochastic differential equation where the coefficients may depend upon the joint law of the state and control. By using feedback
Dynamic Programming for Optimal Control of Stochastic McKean-Vlasov Dynamics
TLDR
A dynamic programming principle for the value function in the Wasserstein space of probability measures, which is proved from a flow property of the conditional law of the controlled state process, and the viscosity property is proved together with a uniqueness result for thevalue function.
Linear-quadratic McKean-Vlasov stochastic control problems with random coefficients on finite and infinite horizon, and applications *
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems , and allow notably some
MFG model with a long-lived penalty at random jump times: application to demand side management for electricity contracts
We consider an energy system with n consumers who are linked by a Demand Side Management (DSM) contract, i.e. they agreed to diminish, at random times, their aggregated power consumption by a
Portfolio Selection with Transaction Costs
TLDR
It is shown that the optimal buying and selling policies are the local times of the two-dimensional process of bank and stock holdings at the boundaries of a wedge-shaped region which is determined by the solution of a nonlinear free boundary problem.
Structural default model with mutual obligations
TLDR
This paper develops a simple structural default model with banks’ assets driven by correlated multidimensional Brownian motion with drift and demonstrates that mutual obligations have noticeable impact on the system behavior.
Control of McKean–Vlasov dynamics versus mean field games
We discuss and compare two investigation methods for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two
...
...