Box-constrained vector optimization: a steepest descent method without “a priori” scalarization

In this paper a notion of descent direction for a vector function defined on a box is introduced. This concept is based on an appropriate convex combination of the “projected” gradients of the components of the objective functions. The proposed approach does not involve an “apriori” scalarization since the coefficients of the convex combination of the projected gradients are the solutions of a suitable minimization problem depending on the feasible point considered. Subsequently, the descent directions are considered in the formulation of a first order optimality condition for Pareto optimality in a box-constrained multiobjective optimization problem. Moreover, a computational method is proposed to solve box-constrained multiobjective optimization problems. This method determines the critical points of the box constrained multiobjective optimization problem following the trajectories defined through the descent directions mentioned above. The convergence of the method to the critical points is proved. The numerical experience shows that the computational method efficiently determines the whole local Pareto front.Multi-objective optimization problems, path following methods, dynamical systems, minimal selection.

From bond yield to macroeconomic instability: A parsimonious affine model

We present a hybrid Heston model with a common stochastic volatility to describe government bond yield dynamics. The model is analytically tractable and, therefore, can be efficiently estimated using the maximum likelihood approach and a specific expansion in order to cope with the curse of dimensionality. Twofold is the model contribution. First, it captures changes in the yield volatility and predict future yield values of Germany, French, Italy and Spain. The result is an early-warning indicator which anticipates phases of instability characterizing the time series investigated. Then, the model describes convergence/divergence phenomena among European government bond yields and explores the countries’ reactions to a common monetary policy described through the EONIA interbank rate. We also investigate the potential of this indicator on U.S. data (treasury bills).The research leading to these results has received funding from the European Union, Seventh Framework Programme FP7, under grant agreement FinMaP no. 612955

A calibration procedure for analyzing stock price dynamics in an agent-based framework

In this paper we introduce a calibration procedure for validating of agent based models. Starting from the well-known financial model of (Brock and Hommes, 1998), we show how an appropriate calibration enables the model to describe price time series. We formulate the calibration problem as a nonlinear constrained optimization that can be solved numerically via a gradient-based method. The calibration results show that the simplest version of the Brock and Hommes model, with two trader types, fundamentalists and trend-followers, replicates nicely the price series of four different markets indices: the S&P 500, the Euro Stoxx 50, the Nikkei 225 and the CSI 300. We show how the parameter values of the calibrated model are important in interpreting the trader behavior in the different markets investigated. These parameters are then used for price forecasting. To further improve the forecasting, we modify our calibration approach by increasing the trader information set. Finally, we show how this new approach improves the model׳s ability to predict market prices

Taming financial systemic risk: models, instruments and early warning indicators

In recent decades, most advanced and developing economies have suffered—or are still suffering—from profound and repeated crises. The literature has reflected on the determinants of these perturbations by placing particular emphasis on the malfunctioning of either the real or financial sphere of the economy. The main research question has been to understand whether it was the real economy that perturbed finance sectors or, alternatively, the financial/credit market that depressed real production. Whatever the direction of the causality nexus and, consequently the origin of the attack, with some studies identifying the direction from real markets to financial sectors (see Bernanke and Gertler 1989; Greenwald and Stiglitz 1993; Delli Gatti et al. 2012) and others reversing it (see Christiano and Ikeda 2011; Brunnermeier et al. 2012), what is certainly undoubted is the self-reinforcing interaction between the two sectors, which translates into booms followed by busts. In light of this, part of the literature has not focused as much on the origin of crises, but rather on the mechanisms of shock propagation. In this regard, many studies have shown that a combination of forces is needed to generate shock transmission. Specifically, the literature on contagion has shown that agents’ interaction and the emerging network topology are key ingredients for the spread of systemic risk (see, for instance, Lux 2016; Lux and Montagna 2017). The interaction has in fact been recognized as generating two opposing effects: risk sharing, which decreases with connectivity, and systemic risk, which in contrast, increases with linkages (see, for instance, Allen and Gale 2000; Battiston et al. 2007, 2012a, b; Grilli et al. 2014; Iori et al. 2006; Mazzarisi et al. 2020; Tedeschi et al. 2012). Many other studies have confirmed the nonlinearity of this relationship. This body of work has also shown that other factors must be added to generate the catastrophic effects that characterized the 2007 financial collapse, namely the agents’ heterogeneity and financial fragility (see Aymanns et al. 2016; Bardoscia et al. 2017; Caccioli et al. 2011, 2014, 2015; Lenzu and Tedeschi 2012). In fact, as reported by Berardi and Tedeschi (2017) “on the one hand, the possible emergence of contagion depends crucially on the degree of heterogeneity. Indeed, when the agents’ balance sheets are heterogeneous, banks are not uniformly exposed to their counter-party. Therefore, if contagion is triggered by the failure of a big bank, which represents the highest source of exposure for its creditors, the situation is certainly worse than when agents are homogeneous [...]. On the other hand, the probability of default in credit markets is strictly linked to the presence of highly leveraged agents [...]. Indeed, when variations in the level of financial robustness of institutions tend to persist in time or to get amplified, financial linkages among financially fragile banks represent a propagation channel for contagion and a source of systemic risk.” Interestingly enough, this second element is very close in spirit to the Minskyan financial instability hypothesis, where endogenous shifts in the degree of financial fragility of agents generate business fluctuations and, possibly, the materialization of bankruptcy cascades (see Minsky 1964; Ferri and Minsky 1992)

Bank's strategies during the financial crisis

In this paper we introduce a calibration procedure suitable for the validation of agent based models. Starting from the well-known financial model of Brock and Hommes 1998, we show how an appro- priate calibration technique makes the model able to describe price time series.The calibration results show that the simplest version of the Brock and Hommes model, with two trader types, fundamentalists and trend-followers, well replicates the price series of four sub-sectoral banking indexes, representing different geographical areas. Moreover, we show how the parameter values of the calibrated model are important to analyse the trader behavior on the different investigated markets

Toll like receptor signaling in "inflammaging": microRNA as new players.

none7nopubblicazione scientificaopenOlivieri F; Rippo MR; Prattichizzo F; Babini L; Graciotti L; Recchioni R; Procopio ADOlivieri, Fabiola; Rippo, Maria Rita; Prattichizzo, Francesco; Babini, Lucia; Graciotti, Laura; Recchioni, R; Procopio, Antonio Domenic

The Calibration of Some Stochastic Volatility Models Used in Mathematical Finance

Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a stochastic differential Equation. The volatility of the asset price itself is modeled as a stochastic process depending on time whose dynamics is described by a stochastic differential Equation. The stochastic differential Equations for the asset price and for the volatility are coupled and together with the necessary initial conditions and correlation assumptions constitute the model. Note that the stochastic volatility is not observable in the financial markets. In order to use these models, for example, to evaluate prices of derivatives on the asset or to forecast asset prices, it is necessary to calibrate them. That is, it is necessary to estimate starting from a set of data the values of the initial volatility and of the unknown parameters that appear in the asset price/volatility dynamic Equations. These data usually are observations of the asset prices and/or of the prices of derivatives on the asset at some known times. We analyze some stochastic volatility models summarizing merits and weaknesses of each of them. We point out that these models are examples of stochastic state space models and present the main techniques used to calibrate them. A calibration problem for the Heston model is solved using the maximum likelihood method. Some numerical experiments about the calibration of the Heston model involving synthetic and real data are presented

A Video Game Based on Optimal Control and Elementary Statistics

The video game presented in this paper is a prey-predator game where two preys (human players) must avoid three predators (automated players) and must reach a location in the game field (the computer screen) called preys' home. The game is a sequence of matches and the human players (preys) must cooperate in order to achieve the best perform- ance against their opponents (predators). The goal of the predators is to capture the preys, which are the predators try to have a "rendez vous" with the preys, using a small amount of the "resources" available to them. The score of the game is assigned following a set of rules to the prey team, not to the individual prey. In some situations the rules imply that to achieve the best score it is convenient for the prey team to sacrifice one of his components. The video game pursues two main purposes. The first one is to show how the closed loop solution of an optimal control problem and elementary sta- tistics can be used to generate (game) actors whose movements satisfy the laws of classical mechanics and whose be- haviour simulates a simple form of intelligence. The second one is "educational", in fact the human players in order to be successful in the game must understand the restrictions to their movements posed by the laws of classical mechanics and must cooperate between themselves. The video game has been developed having in mind as players for children aged between five and thirteen years. These children playing the video game acquire an intuitive understanding of the basic laws of classical mechanics (Newton's dynamical principle) and enjoy cooperating with their teammate. The video game has been experimented on a sample of a few dozen children. The children aged between five and eight years find the game amusing and after playing a few matches develop an intuitive understanding of the laws of classical me- chanics. They are able to cooperate in making fruitful decisions based on the positions of the preys (themselves), of the predators (their opponents) and on the physical limitations to the movements of the game actors. The interest in the game decreases when the age of the players increases. The game is too simple to interest a teenager. The game engine consists in the solution of an assignment problem, in the closed loop solution of an optimal control problem and in the adaptive choice of some parameters. At the beginning of each match, and when necessary during a match, an assign- ment problem is solved, that is the game engine chooses how to assign to the predators the preys to chase. The resulting assignment implies some cooperation among the predators and defines the optimal control problem used to compute the strategies of the predators during the match that follows. These strategies are determined as the closed loop solution of the optimal control problem considered and can be thought as a (first) form of artificial intelligence (AI) of the preda- tors. In the optimal control problem the preys and the predators are represented as point masses moving according to Newton's dynamical principle under the action of friction forces and of active forces. The equations of motion of these point masses are the constraints of the control problem and are expressed through differential equations. The formula- tion of the decision process through optimal control and Newton's dynamical principle allows us to develop a game where the effectiveness and the goals of the automated players can be changed during the game in an intuitive way sim- ply modifying the values of some parameters (i.e. mass, friction coefficient, ...). In a sequence of game matches the predators (automated players) have "personalities" that try to simulate human behaviour. The predator personalities are determined making an elementary statistical analysis of the points scored by the preys in the game matches played and consist in the adaptive choice of the value of a parameter (the mass) that appears in the differential equations that define the movements of the predators. The values taken by this parameter determine the behaviour of the predators and their effectiveness in chasing the preys. The predators personalities are a (second) form of AI based on elementary statistics that goes beyond the intelligence used to chase the preys in a match. In a sequence of matches the predators using this second form of AI adapt their behaviour to the preys' behaviour. The video game can be downloaded from the website: http://www.ceri.uniroma1.it/ceri/zirilli/w10/

Long-term exposure of human endothelial cells to metformin modulates miRNAs and isomiRs.

Increasing evidence suggest that the glucose-lowering drug metformin exerts a valuable anti-senescence role. The ability of metformin to affect the biogenesis of selected microRNAs (miRNAs) was recently suggested. MicroRNA isoforms (isomiRs) are distinct variations of miRNA sequences, harboring addition or deletion of one or more nucleotides at the 5\u27 and/or 3\u27 ends of the canonical miRNA sequence. We performed a comprehensive analysis of miRNA and isomiR profile in human endothelial cells undergoing replicative senescence in presence of metformin. Metformin treatment was associated with the differential expression of 27 miRNAs (including miR-100-5p, -125b-5p, -654-3p, -217 and -216a-3p/5p). IsomiR analysis revealed that almost 40% of the total miRNA pool was composed by non-canonical sequences. Metformin significantly affects the relative abundance of 133 isomiRs, including the non-canonical forms of the aforementioned miRNAs. Pathway enrichment analysis suggested that pathways associated with proliferation and nutrient sensing are modulated by metformin-regulated miRNAs and that some of the regulated isomiRs (e.g. the 5\u27 miR-217 isomiR) are endowed with alternative seed sequences and share less than half of the predicted targets with the canonical form. Our results show that metformin reshapes the senescence-associated miRNA/isomiR patterns of endothelial cells, thus expanding our insight into the cell senescence molecular machinery