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Francesco Cordoni

Publications and source records attributed to Francesco Cordoni.

16 recordsLinked to original sources

Measurements of the micro-spill structure of medical cyclotron and synchrotron beams and its impact on pulse pileup

Detector characterization and instrumentation testing are often performed at cyclotron and synchrotron facilities, many of which were originally developed for medical applications in cancer therapy. For particle physics experiments requiring a single-particle resolution, pileup can significantly degrade data quality, making precise knowledge of the beam time structure essential for selecting appropriate readout parameters. However, such information is often unavailable from the facilities and challenging to determine experimentally. Here, we report measurements of the spill time structure at two medical accelerator facilities using a silicon carbide (SiC) particle sensor coupled to a high-frequency readout system. Owing to its high carrier saturation velocity and the tolerance to large bias voltages, SiC is well suited for fast readout and measurements requiring precise timing. Using a 6 GHz readout with custom SiC diodes, we characterize the micro-spill structure of both cyclotron and synchrotron beams on a sub-nanosecond timescale. The measured arrival-time distributions exhibit modulation with the accelerator RF frequencies, reflecting features of the extraction process. The resolved micro-spill structure enables quantitative estimation of pileup contributions and provides design constraints for future readout electronics. The presented results emphasize the importance of the characterization of the beam time-structure characterization for the development of precise readout systems.

physics.ins-det

Multi-Asset Bubbles Equilibrium Price Dynamics

The price-bubble and crash process formation is theoretically investigated in a two-asset equilibrium model. Sufficient and necessary conditions are derived for the existence of average equilibrium price dynamics of different agent-based models, where agents are distinguished in terms of factor and investment trading strategies. In line with experimental results, we show that assets with a positive average dividend, i.e., with a strictly declining fundamental value, display at the equilibrium price the typical hump-shaped bubble observed in experimental asset markets. Moreover, a misvaluation effect is observed in the asset with a constant fundamental value, triggered by the other asset that displays the price bubble shape when a sharp price decline is exhibited at the end of the market.

q-fin.TR

Action-State Dependent Dynamic Model Selection

A model among many may only be best under certain states of the world. Switching from a model to another can also be costly. Finding a procedure to dynamically choose a model in these circumstances requires to solve a complex estimation procedure and a dynamic programming problem. A Reinforcement learning algorithm is used to approximate and estimate from the data the optimal solution to this dynamic programming problem. The algorithm is shown to consistently estimate the optimal policy that may choose different models based on a set of covariates. A typical example is the one of switching between different portfolio models under rebalancing costs, using macroeconomic information. Using a set of macroeconomic variables and price data, an empirical application to the aforementioned portfolio problem shows superior performance to choosing the best portfolio model with hindsight.

cs.LG

Consistent Causal Inference for High-Dimensional Time Series

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian vector autoregressive process. This is tantamount to assume that the dynamics are captured by a Gaussian copula. No knowledge or estimation of the marginal distribution of the data is required. The procedure consistently identifies the parameters that describe the dynamics of the process and the conditional causal relations among the possibly high dimensional variables under sparsity conditions. The methodology allows us to identify such causal relations in the form of a directed acyclic graph. As illustrative applications we consider the impact of supply side oil shocks on the economy, and the causal relations between aggregated variables constructed from the limit order book on four stock constituents of the S&P500.

stat.ME

Transient impact from the Nash equilibrium of a permanent market impact game

A large body of empirical literature has shown that market impact of financial prices is transient. However, from a theoretical standpoint, the origin of this temporary nature is still unclear. We show that an implied transient impact arises from the Nash equilibrium between a directional trader and one arbitrageur in a market impact game with fixed and permanent impact. The implied impact is the one that can be empirically inferred from the directional trader's trading profile and price reaction to order flow. Specifically, we propose two approaches to derive the functional form of the decay kernel of the Transient Impact Model, one of the most popular empirical models for transient impact, from the behaviour of the directional trader at the Nash equilibrium. The first is based on the relationship between past order flow and future price change, while in the second we solve an inverse optimal execution problem. We show that in the first approach the implied kernel is unique, while in the second case infinite solutions exist and a linear kernel can always be inferred.

q-fin.TR

Stochastic port--Hamiltonian systems

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly different physical domains can be interconnected in order to describe a dynamic system perturbed by general continuous semimartingale. Relevant enough, the noise does not enter into the system solely as an external random perturbation, since each port is itself intrinsically stochastic. Coherently to the classical deterministic setting, we will show how such an approach extends existing literature of stochastic Hamiltonian systems on pseudo-Poisson and pre-symplectic manifolds. Moreover, we will prove that a power-preserving interconnection of stochastic port-Hamiltonian systems is a stochastic port-Hamiltonian system as well.

math.PR

Instabilities in Multi-Asset and Multi-Agent Market Impact Games

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied & Zhang (2019) and Luo & Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied & Zhang (2019) and Luo & Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M ) of markets.

q-fin.TR

A maximum principle for a stochastic control problem with multiple random terminal times

In the present paper we derive, via a backward induction technique, and ad hoc maximum principle for an optimal control problem with multiple random terminal times. Therefore we apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time. Eventually all the above results are applied to a system of interconnected banks.

math.OC

Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion

We consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by the celebrated FitzHugh-Nagumo model, with nonlinear diffusion term, perturbed by a linear multiplicative Brownian-type noise. The main novelty of the present paper relies on the application of the {\it rescaling method} which allows us to reduce the original problem to a random optimal one.

math.OC

A bank salvage model by impulse stochastic controls

The present paper is devoted to the study of a bank salvage model with finite time horizon and subjected to stochastic impulse controls. In our model, the bank's default time is a completely inaccessible random quantity generating its own filtration, then reflecting the unpredictability of the event itself. In this framework the main goal is to minimize the total cost of the central controller who can inject capital to save the bank from default. We address the latter task showing that the corresponding quasi-variational inequality (QVI) admits a unique viscosity solution, Lipschitz continuous in space and Holder continuous in time. Furthermore, under mild assumptions on the dynamics the smooth-fit $W^{(1,2),p}_{loc}$ property is achieved for any $1<p<+\infty$.

q-fin.MF

A lending scheme for a system of interconnected banks with probabilistic constraints of failure

We derive a closed form solution for an optimal control problem related to an interbank lending schemes subject to terminal probability constraints on the failure of banks which are interconnected through a financial network. The derived solution applies to a real banks network by obtaining a general solution when the aforementioned probability constraints are assumed for all the banks. We also present a direct method to compute the systemic relevance parameter for each bank within the network.

q-fin.MF

Asymptotic expansion for some local volatility models arising in finance

In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders. Moreover, we perform a detailed numerical analysis, with accuracy comparisons, of the obtained results by mean of the standard Monte Carlo technique as well as exploiting the polynomial Chaos Expansion approach.

math.PR

Optimal control for the stochastic FitzHugh-Nagumo model with recovery variable

In the present paper we derive the existence and uniqueness of a solution for the optimal control problem determined by a stochastic FitzHugh-Nagumo equation with recovery variable. In particular due the cubic non-linearity in the drift coefficients, standard techniques cannot be applied so that the Ekeland's variational principle has to be exploited.

math.PR

A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps

We consider a stochastic functional delay differential equation, namely an equation whose evolution depends on its past history as well as on its present state, driven by a pure diffusive component plus a pure jump Poisson compensated measure. We lift the problem in the infinite dimensional space of square integrable Lebesgue functions in order to show that its solution is an $L^2-$valued Markov process whose uniqueness can be shown under standard assumptions of locally Lipschitzianity and linear growth for the coefficients. Coupling the aforementioned equation with a standard backward differential equation, and deriving some ad hoc results concerning the Malliavin derivative for systems with memory, we are able to derive a non--linear Feynman--Kac representation theorem under mild assumptions of differentiability.

math.PR

Stochastic reaction-diffusion equations on networks with dynamic time-delayed boundary conditions

We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product Hilbert space, for which we prove the existence and uniqueness of a mild solution. Eventually, a stochastic optimal control application is studied.

math.PR

A stochastic approach to path-dependent nonlinear Kolmogorov equations via BSDEs with time-delayed generators and applications to finance

We prove the existence of a viscosity solution of the following path dependent nonlinear Kolmogorov equation: \[ \begin{cases} \partial_{t}u(t,\phi)+\mathcal{L}u(t,\phi)+f(t,\phi,u(t,\phi),\partial_{x}u(t,\phi) \sigma(t,\phi),(u(\cdot,\phi))_{t})=0,\;t\in[0,T),\;\phi\in\mathbb{\Lambda}\, ,u(T,\phi)=h(\phi),\;\phi\in\mathbb{\Lambda}, \end{cases} \] where $\mathbb{\Lambda}=\mathcal{C}([0,T];\mathbb{R}^{d})$, $(u(\cdot ,\phi))_{t}:=(u(t+\theta,\phi))_{\theta\in[-\delta,0]}$ and \[ \mathcal{L}u(t,\phi):=\langle b(t,\phi),\partial_{x}u(t,\phi)\rangle+\dfrac {1}{2}\mathrm{Tr}\big[\sigma(t,\phi)\sigma^{\ast}(t,\phi)\partial_{xx} ^{2}u(t,\phi)\big]. \] The result is obtained by a stochastic approach. In particular we prove a new type of nonlinear Feynman-Kac representation formula associated to a backward stochastic differential equation with time-delayed generator which is of non-Markovian type. Applications to the large investor problem and risk measures via $g$-expectations are also provided.

math.PR