11 citations · 31 across the 9 of their papers we have counts for
9 papers
On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models
Alexander Kalinin, Thilo Meyer-Brandis, Annika Steibel
We present a tractable class of one-dimensional McKean-Vlasov equations that allow for unique strong solutions and extend the dynamics of various SIS epidemic models that are well-…
The oriented derivative
Alexander Kalinin
We show that the derivatives in the sense of Fréchet and Gâteaux can be viewed as derivatives oriented towards a star convex set with the origin as center. The resulting oriented d…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs in arbitrary moments
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We deduce stability and pathwise uniqueness for a McKean-Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Li…
Mild to classical solutions for XVA equations under stochastic volatility
Damiano Brigo, Federico Graceffa, Alexander Kalinin
We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingal…
Stability, uniqueness and existence of solutions to McKean-Vlasov SDEs: a multidimensional Yamada-Watanabe approach
Alexander Kalinin, Thilo Meyer-Brandis, Frank Proske
We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean-Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic c…
Support characterization for regular path-dependent stochastic Volterra integral equations
Alexander Kalinin
We consider a stochastic Volterra integral equation with regular path-dependent coefficients and a Brownian motion as integrator in a multidimensional setting. Under an imposed abs…
On the support of solutions of stochastic differential equations with path-dependent coefficients
Rama Cont, Alexander Kalinin
Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given…
Markovian Integral Equations
Alexander Kalinin
We analyze multidimensional Markovian integral equations that are formulated with a time-inhomogeneous progressive Markov process that has Borel measurable transition probabilities…
Mild and viscosity solutions to semilinear parabolic path-dependent PDEs
Alexander Kalinin, Alexander Schied
We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appear…