6 papers · 1 filter
On (fake) Stationarity in Stochastic Volterra Equations with Affine Drift and Regular Kernels
Emmanuel Gnabeyeu, Gilles Pagès
We investigate the fake stationarity properties of solutions to forward Stochastic Volterra Integral Equations (SVIEs) with affine drift and long-memory (regular) kernels, both on…
Optimal Merton's Problem under Multivariate Affine Volterra Models with Jumps
Sigui Brice Dro, Emmanuel Gnabeyeu
This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate th…
On Path-dependent Volterra Integral Equations: Strong Well-posedness and Stochastic Numerics
Emmanuel Gnabeyeu, Gilles Pagès
The aim of this paper is to provide a comprehensive analysis of the path-dependent Stochastic Volterra Integral Equations (SVIEs), in which both the drift and the diffusion coeffic…
On explicit solutions to a class of quadratic BSDEJs driven by affine Volterra processes with jumps and applications
Sigui Brice Dro, Emmanuel Gnabeyeu
In this paper we consider a class of quadratic BSDEs with jumps (quadratic BSDEJs) involving inhomogeneous affine Volterra processes and show that their solution can be reduced to…
On Utility Maximization under Multivariate Fake Stationary Affine Volterra Models
Emmanuel Gnabeyeu
This paper is concerned with Merton's portfolio optimization problem in a Volterra stochastic environment described by a multivariate fake stationary Volterra--Heston model. Due to…
Fake stationary rough Heston volatility: Microstructure-inspired foundations
Emmanuel Gnabeyeu, Gilles Pagès, Mathieu Rosenbaum
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate s…