Background
I am a PhD student in Mathematics. I am a member of the STORM project and I started working at UiO in August 2018 under the supervision of Giulia Di Nunno. My main interest is stochastic control theory, especially in connection with time change. Currently, I am working with optimization of Volterratype dynamics motivated by applications in finance. In particular, I am working with finite and infinite dimensional settings, and studied several optimization techniques for both optimal control and game theory.
Before coming to Oslo I graduated in Mathematics at the University of Pisa with a thesis entitled “Classes of Stochastic Volterra Processes”. The main goal of the thesis was the study of some known classes of Volterra processes, with particular interest to application to finance, and the introduction of jumps in a known setting.
Preprints
 Backward Volterra equations with timechanged Lévy noise and maximum principles, Joint work with Giulia Di Nunno
 Maximum principles for stochastic timechanged Volterra games,
Joint work with Giulia Di Nunno
 Lifting of Volterra processes: optimal control and HJB equations,
Joint work with Giulia Di Nunno
 Maximum principles for infinite dimensional timechanged processes,
Joint work with Giulia Di Nunno
Tags:
Mathematics,
Mathematical Finance,
Stochastic Analysis
Publications

Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations.
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Based on a joint work with Giulia Di Nunno

Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations.
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We want to maximize a performance functional, with dynamics of the underlying forward process of Volterra type. Due to this assumption, the system is not Markovian, and one cannot apply directly the dynamic programming principle (DPP). In order to recover the DPP, we introduce a lift that allows us to get some Markov properties by rewriting the forward process' dynamics in a Banach space setting. Once we reformulated the problem in the new setting, we deduce a DPP for the lifted problem and obtain the corresponding infinite dimensional HJB equations. We go back to the initial real valued problem and characterize the optimal control of the original problem in terms of the solution of the lifted one. Examples and applications will be presented. Joint work with Giulia di Nunno

Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations.
Show summary
Based on a joint work with Giulia di Nunno

Giordano, Michele (2020). Lifts of Volterra processes: optimal control and HJB equations.
Show summary
Based on a joint work with Giulia Di Nunno

Giordano, Michele (2020). Maximum Principles for Stochastic Time Changed Volterra Games.
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We establish a framework for the study of forwardbackward stochastic Volterra integral games (FBSVIG) driven by timechanged Lévy noises. We use a maximum principle approach in order to find the Nash equilibriums of a two player game based on a forward equation and a backward equation for each player. Since we work with time change, we deal with two information flows and we consider one filtration to have partial information respect to the other. Examples will be provided. Joint work with Giulia di Nunno Based on a joint work with Giulia di Nunno

Giordano, Michele (2019). A Maximum Principle for Volterra Time Changed Processes.

Giordano, Michele (2019). A Maximum Principle for Volterra Time Changed Processes.

Giordano, Michele (2019). A Maximum principle for Volterra Time Changed Processes.

Giordano, Michele (2019). A Maximum principle for Volterra Time Changed Processes.
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We establish a framework for the study of backward stochastic Volterra integral equations (BSVIE) driven by timechanged Lévy noises. In fact we shall consider a random measure $\mu$ that can be decomposed as the sum of a conditional Gaussian measure and a conditional centered Poisson measure. In this paper we deal with two information flows: $F_t$ namely the smallest right continuous filtration to which $\mu$ is adapted, $G_t$, generated by $\mu$ and the entire history of the time change processes, and we shall consider the information $F$ as partial with respect to $G$. Given a controlled dynamic, we will consider the optimization problem of finding the supremum of a functional $J(u)$ for a suitable control set $A$ which we consider to be either $F$ or $G$ predictable. We prove both a sufficient and a necessary maximum principle for such performance functional, showing that in the $F$predictable case we can find a solution by projecting the results obtained for the $G$predictable case onto the $F$predictable one. We shall make use of stochastic derivatives. We stress that we cannot use the classical Malliavin calculus as our integrators are not the Brownian motion nor the centered Poisson random measure. Indeed we could use a conditional form of such calculus as introduced by Yablonski, however we resolve by using the nonanticipating derivative introduced and for martingale random fields as integrators. The use of the nonanticipating derivative has also the advantage that we do not require more restrictive conditions on domains, since it is already well defined for all $L^2(P)$ random variables. When studying such problems, we come across a BSVIE driven by a noise $\mu$ as above: we prove existence and uniqueness results for such BSVIE and we compute an explicit solution in the linear case. Examples and applications will be presented.

Giordano, Michele (2019). A Maximum principle for Volterra time changed processes.
Published Aug. 23, 2018 3:28 PM
 Last modified Dec. 14, 2020 9:37 AM