In this paper, we study the classical problem of the first hitting time density to a moving
boundary for a diffusion process, which satisfies the Cherkasov condition, and hence, can be …

We develop an Euler-type particle method for the simulation of a McKean--Vlasov equation
arising from a mean-field model with positive feedback from hitting a boundary. Under …

In this article, we use recently developed extension of the classical heat potential method in
order to solve three important but seemingly unrelated problems of financial engineering: (a) …

The supercooled Stefan problem and its variants describe the freezing of a supercooled
liquid in physics, as well as the large system limits of systemic risk models in finance and of …

In this paper, we study the classical problem of the first passage hitting density of an
Ornstein--Uhlenbeck process. We give two complementary (forward and backward) formulations of …

In this paper, we study the nonlinear diffusion equation associated with a particle system
where the common drift depends on the rate of absorption of particles at a boundary. We …

We consider a structural default model in an interconnected banking network as in [1], with
mutual obligations between each pair of banks. We analyse the model numerically for two …

We derive a semi-analytical formula for the transition probability of three-dimensional Brownian
motion in the positive octant with absorption at the boundaries. Separation of variables in …

In this paper, we study the non-linear diffusion equation associated with a particle system
where the common drift depends on the rate of absorption of particles at a boundary. We …

In this paper, we study the non-linear diffusion equation associated with a par-5 ticle system
where the common drift depends on the rate of absorption of particles 6 at a boundary. We …