13 citations · 26 across the 6 of their papers we have counts for
6 papers
Convergence of a time-stepping scheme to the free boundary in the supercooled Stefan problem
Vadim Kaushansky, Christoph Reisinger, Mykhaylo Shkolnikov +1
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…
On the First Hitting Time Density of an Ornstein-Uhlenbeck Process
Alexander Lipton, Vadim Kaushansky
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…
Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary
Alexander Lipton, Vadim Kaushansky, Christoph Reisinger
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…
Simulation of particle systems interacting through hitting times
Vadim Kaushansky, Christoph Reisinger
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 assum…
Transition probability of Brownian motion in the octant and its application to default modeling
Vadim Kaushansky, Alexander Lipton, Christoph Reisinger
We derive a semi-analytic formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variab…
Numerical analysis of an extended structural default model with mutual liabilities and jump risk
Vadim Kaushansky, Alexander Lipton, Christoph Reisinger
We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obliga…