Estimating risks of European option books using neural-SDE market models by Cohen, SN, Reisinger, C, Wang, S

“…In this paper we examine the capacity of arbitrage-free neural stochastic differential equation market models to produce realistic scenarios for the joint dynamics of multiple European options on a single underlying. …”

A numerical scheme for the quantile hedging problem by Bénézet, C, Chassagneux, J-F, Reisinger, C

“…We prove convergence in the monotone case combining backward stochastic differential equation arguments with the Barles and Jakobsen and Barles and Souganidis approaches for nonlinear PDEs. …”

Exponential integrability properties of euler discretization schemes for the Cox-Ingersoll-Ross process by Cozma, A, Reisinger, C

“…These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.…”

Milstein schemes and antithetic multilevel Monte Carlo sampling for delay McKean–Vlasov equations and interacting particle systems by Bao, J, Reisinger, C, Ren, P, Stockinger, W

“…In this paper, we first derive Milstein schemes for an interacting particle system associated with point delay McKean–Vlasov stochastic differential equations, possibly with a drift term exhibiting super-linear growth in the state component. …”

First order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems by Bao, J, Reisinger, C, Ren, P, Stockinger, W

“…In this paper, we derive fully implementable first order time-stepping schemes for McKean–Vlasov stochastic differential equations (McKean–Vlasov SDEs), allowing for a drift term with super-linear growth in the state component. …”

An explicit Milstein-type scheme for interacting particle systems and McKean--Vlasov SDEs with common noise and non-differentiable drift coefficients by Biswas, S, Kumar, C, Neelima, Dos Reis, G, Reisinger, C

“…We propose an explicit drift-randomised Milstein scheme for both McKean–Vlasov stochastic differential equations and associated high-dimensional interacting particle systems with common noise. …”

Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative by Reisinger, C

“…In this article, we extend a Milstein finite difference scheme introduced in 8 for a certain linear stochastic partial differential equation (SPDE) to semi-implicit and fully implicit time-stepping as introduced by Szpruch 32 for stochastic differential equations (SDEs). We combine standard finite difference Fourier analysis for partial differential equations with the linear stability analysis in 3 for SDEs to analyse the stability and accuracy. …”

An adaptive Euler–Maruyama scheme for McKean–Vlasov SDEs with super-linear growth and application to the mean-field FitzHugh–Nagumo model by Reisinger, C, Stockinger, W

“…In this paper, we introduce fully implementable, adaptive Euler–Maruyama schemes for McKean–Vlasov stochastic differential equations (SDEs) assuming only a standard monotonicity condition on the drift and diffusion coefficients but no global Lipschitz continuity in the state variable for either, while global Lipschitz continuity is required for the measure component. …”

Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems by Reisinger, C, Zhang, Y

“…In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network (DNN), whose complexity grows at most polynomially in both the dimension of the state equation and the reciprocal of the required accuracy. …”

Linear convergence of a policy gradient method for some finite horizon continuous time control problems by Reisinger, C, Stockinger, W, Zhang, Y

“…The proof exploits careful regularity estimates of backward stochastic differential equations.…”

Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift by Leobacher, G, Reisinger, C, Stockinger, W

“…In this paper, we first establish well-posedness results for one-dimensional McKean–Vlasov stochastic differential equations (SDEs) and related particle systems with a measure-dependent drift coefficient that is discontinuous in the spatial component, and a diffusion coefficient which is a Lipschitz function of the state only. …”

Well-posedness and tamed schemes for McKean-Vlasov equations with common noise by Kumar, C, Neelima, Reisinger, C, Stockinger, W

“…In this paper, we first establish well-posedness of McKean–Vlasov stochastic differential equations (McKean–Vlasov SDEs) with common noise, possibly with coefficients of super-linear growth in the state variable. …”

A posteriori error estimates for fully coupled McKean–Vlasov forward-backward SDEs by Reisinger, C, Stockinger, W, Zhang, Y

“…Fully coupled McKean–Vlasov forward-backward stochastic differential equations (MV-FBSDEs) arise naturally from large population optimization problems. …”

Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models by Cozma, A

“…We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. …”