24 citations · 26 across the 29 of their papers we have counts for
32 papers
Hölder regularity for backward stochastic Volterra integral equations and applications to numerical schemes
Pere Diaz-Lozano, Giulia Di Nunno
We prove a Hölder-type regularity estimate for the martingale integrand of a backward stochastic Volterra integral equation (BSVIE). The estimate is formulated in after av…
An Euler scheme for BSDEs via the Wiener chaos decomposition
Pere Diaz-Lozano, Giulia Di Nunno
The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each ti…
Deep Operator BSDE: a Numerical Scheme to Approximate Solution Operators
Pere Diaz-Lozano, Giulia Di Nunno
Motivated by dynamic risk measures and conditional -expectations, in this work we propose a numerical method to approximate the solution operator given by a Backward Stochastic…
Insights on Stochastic Dynamics for Transmission of Monkeypox: Biological and Probabilistic Behaviour
Ghaus ur Rahman, Olena Tymoshenko, Giulia Di Nunno
The transmission of monkeypox is studied using a stochastic model taking into account the biological aspects, the contact mechanisms and the demographic factors together with the i…
Utility maximisation and change of variable formulas for time-changed dynamics
Giulia Di Nunno, Hannes Haferkorn, Asma Khedher +1
In this paper we derive novel change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion where we assume that the time-change is a general increasin…
Cash non-additive risk measures: horizon risk and generalized entropy
Giulia Di Nunno, Emanuela Rosazza Gianin
Horizon risk (see arXiv:2301.04971) is studied in the context of cash non-additive fully-dynamic risk measures induced by BSDEs. Furthermore, we introduce a risk measure based on g…
Power law in Sandwiched Volterra Volatility model
Giulia Di Nunno, Anton Yurchenko-Tytarenko
In this paper, we present analytical proof demonstrating that the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behavior of the at-the-money implied…
From constant to rough: A survey of continuous volatility modeling
Giulia Di Nunno, Kęstutis Kubilius, Yuliya Mishura +1
In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the…
Lifting of Volterra processes: optimal control in UMD Banach spaces
Giulia di Nunno, Michele Giordano
We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply…
Fully-dynamic risk measures: horizon risk, time-consistency, and relations with BSDEs and BSVIEs
Giulia Di Nunno, Emanuela Rosazza Gianin
In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the p…
Sandwiched Volterra Volatility model: Markovian approximations and hedging
Giulia Di Nunno, Anton Yurchenko-Tytarenko
We consider stochastic volatility dynamics driven by a general Hölder continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the expli…
Option pricing in Sandwiched Volterra Volatility model
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model…
Before and after default: information and optimal portfolio via anticipating calculus
José A. Salmerón, Giulia Di Nunno, Bernardo D'Auria
Default risk calculus plays a crucial role in portfolio optimization when the risky asset is under threat of bankruptcy. However, traditional stochastic control techniques are not…
The heat modulated infinite dimensional Heston model and its numerical approximation
Fred Espen Benth, Gabriel Lord, Giulia Di Nunno +1
The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite d…
SPDE bridges with observation noise and their spatial approximation
Giulia Di Nunno, Salvador Ortiz-Latorre, Andreas Petersson
This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solu…
Sandwiched SDEs with unbounded drift driven by Hölder noises
Giulia Di Nunno, Yuliya Mishura, Anton Yurchenko-Tytarenko
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. The corresponding equation turns out to have a unique…
Maximum principles for stochastic time-changed Volterra games
Giulia Di Nunno, Michele Giordano
We study a stochastic differential game between two players, controlling a forward stochastic Volterra integral equation (FSVIE). Each player has to optimize his own performance fu…
Stochastic Volterra equations with time-changed Lévy noise and maximum principles
Giulia di Nunno, Michele Giordano
Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed Lévy noises, which are in general no…
Path-dependent Kyle equilibrium model
José M. Corcuera, Giulia Di Nunno
We consider an auction type equilibrium model with an insider in line with the one originally introduced by Kyle in 1985 and then extended to the continuous time setting by Back in…
Utility maximisation and time-change
Giulia Di Nunno, Hannes Haferkorn, Asma Khedher +1
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian mot…
Fully-dynamic risk-indifference pricing and no-good-deal bounds
Jocelyne Bion-Nadal, Giulia Di Nunno
The seller's risk-indifference price evaluation is studied. We propose a dynamic risk-indifference pricing criteria derived from a fully-dynamic family of risk measures on the $L_p…
Stochastic functional differential equations and sensitivity to their initial path
David R. Baños, Giulia Di Nunno, Hannes Haferkorn +1
We consider systems with memory represented by stochastic functional differential equations. Substantially, these are stochastic differential equations with coefficients depending…
Fractional calculus and path-wise integration for Volterra processes driven by Lévy and martingale noise
Giulia Di Nunno, Yuliya Mishura, Konstiantyn Ralchenko
We introduce a pathwise integration for Volterra processes driven by Lévy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes…
A Maximum Principle for Mean-Field SDEs with time change
Giulia Di Nunno, Hannes Haferkorn
Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existenc…