Abstract: Variable annuities are life-insurance contracts designed to meet long-term investment goals. Such contracts provide several financial guarantees to the policyholder. A minimum rate is guaranteed by the insurer in order to protect the policyholder’s capital against market downturns. Moreover, the policyholder has the right to early terminate the contract (early surrender) and to receive the account value. In general, a penalty, which decreases in time, is applied by the insurer in case of early surrender. We provide a theoretical analysis of variable annuities with a focus on the holder’s right to an early termination of the contract. We obtain a rigorous pricing formula and the optimal exercise boundary for the surrender option. We also illustrate our theoretical results with extensive numerical experiments. The pricing problem is formulated as an optimal stopping problem with a time-dependent payoff, which is discontinuous at the maturity of the contract. This structure leads to non-monotone optimal stopping boundaries, which we prove nevertheless to be continuous. Because of this lack of monotonicity, we cannot use classical methods from optimal stopping theory and, thus, we contribute a new methodology for non-monotone stopping boundaries.

This is a joint work with T. De Angelis and G. Stabile.

- when: 25 September 2024, at 16.00

- where: room 206 campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

- on-line: meet.google.com/taq-hsgp-fyi

Link Flyer

Abstract: The capital allocation problem of an insurance company relates to the decomposition of an aggregate risk capital into additive contributions corresponding to different risk sources (e.g., individual agents, business units, specific guarantees included in a set of contracts). The proportions of risk capital allocated to each part can be viewed as quantitative descriptions of the components of a whole, subject to a fixed sum constraint (full allocation). This interpretation suggests interesting connections between capital allocation principles and Compositional Data (CoDa) analysis. The purpose of this work is to introduce a novel allocation framework that prioritizes the compositional perspective. In particular, we propose an optimality criterion based on a (modified) compositional distance between relative losses and capital shares allocated to them. In this way, we explicitly recognize that the relevant information associated with risks arising from –and resources assigned to– each constituent part is indeed information relative to a total. Different from previous research on compositional capital allocations, our approach is not restricted to gradient allocation rules or specific risk measures like VaR or CVaR. We propose instead a general reformulation of the optimal capital allocation problem which is inherently consistent with the relative scale of compositional variables. The resulting capital allocation solutions are compared to other proposals in recent literature and evaluated empirically on a dataset of cyber losses.

- when: 9 October 2024, at 16.15

- where: 206 campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

- on-line: meet.google.com/eic-tuux-rzh

Link Flyer

Abstract: In recent years, there has been a notable surge of Environmental, Social, and Governance (ESG) investing. This paper provides a simple and comprehensive tool to tackle the issue of missing ESG data. Firstly, it allows to shed light on the failure of ESG ratings due to data sparsity. Exploiting machine learning techniques, we find that the most significant metrics are promises, targets and incentives, rather than realized variables. Then, data incompleteness is addressed, which affects about 50% of the overall dataset. Via a new methodology, imputation accuracy is improved with respect to traditional median-driven techniques. Lastly, exploiting the newly imputed data, a quantitative dimension of greenwashing is introduced. We show that when rating agencies do not efficiently impute missing metrics, ESG scores carry a quantitative bias that should be accounted by market players. 

- when: 18 July 2024, at 15.00

- where: room 205, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer  Link Slides

Abstract: In this talk, we investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Using several assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we discuss the reward generalization property of the proposed Multi-Objective algorithm, preliminary statistical evidence for its predictive stability over the corresponding Single-Objective strategy, and its performance for sparse reward mechanisms.

Joint work with C. Disselkamp (pagent.ai), D. Scassola (aindo, and Università degli Studi di Trieste), and C. Helf (pagent.ai).

- when: 18 July 2024, at 14.00

- where: room 205, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer  Link Slides

Abstract: Regression analysis offers tools for explaining the relation between (a set of) dependent and independent variables. Recent advances extend the available response types from uni- or multivariate to functional, and more recently also distributional responses. For functional distributions, often represented through probability density functions, the Bayes space framework was developed to respect the relative information they carry. The Hilbert space structure of Bayes space enables one to utilize standard methods of functional data analysis for the use on - properly transformed - density functions. Focusing on regression analysis, it is possible to construct adequate models with densities on the side of both the dependent and independent variables.

In this seminar, a brief overview of regression models for univariate densities will be presented. A closer attention will be given to the possible generalization of additive regression model for bivariate distributions. Finally, an outlook at the Bayesian inference in linear regression with probability densities will be discussed. All proposed methods will be demonstrated on real data from the fields of geochemistry and demographics.

- when: 23 May, at 15.00

- where: room 204, via Perrone, 18, Novara

Link Flyer  Link Slides

 Abstract: On 14 May 2024, a short course with Jitka Machalova and Karel Hron from "Palacký University Olomouc, Czech Republic" and Alessandra Menafoglio from "Politecnico di Milano, Italy" on the topic of Bayes spaces and their recent developments will be held in presence at the "Dipartimento di Studi per l'Economia e l'Impresa" of the "Università del Piemonte Orientale" and streamed online.

The analysis of distributional data (probability density functions or histogram data) has recently gained increasing attention in the applications. Distributional data are often observed by themselves, or as result of aggregation of large streams of data. The short course will provide an introduction to the analysis of these data using a Functional Data Analysis (FDA) approach, grounded on the perspective of Bayes spaces. These spaces are mathematical spaces whose points are densities (or, more generally, measures), which generalize to the FDA setting the Aitchison simplex for multivariate compositional data. The course will give an overview of the theory of Bayes spaces in their univariate and multivariate settings. All FDA methods, presented there, will be illustrated through examples from real case studies.

The short course, that will be streamed live, will provide an opportunity to gain new insight into FDA of univariate and multivariate density functions through lens of the Bayes spaces methodology.

All the interested are invited to attend in-site or online to the first "Density Data Analysis meeting" on the 3rd June 2024. More information here.

• when: 14 May 2024, at 10.30 - 13.30 (time zone Europe/Rome)

• where: room 205, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale

Link Flyer  Link Slides

Abstract: The fuzzy approach to clustering arises to cope with situations where objects have not a clear assignment. Unlike the hard/standard approach where each object can only belong to exactly one cluster, in a fuzzy setting, the assignment is soft; that is, each object is assigned to all clusters with certain membership degrees varying in the unit interval. The best known fuzzy clustering algorithm is the fuzzy k-means (FkM), or fuzzy c-means. It is a generalization of the classical k-means method. Starting from the FkM algorithm, and in more than 40 years, several variants have been proposed. The peculiarity of such different proposals depends on the type of data to deal with, and on the cluster shape. The aim is to show fuzzy clustering alternatives to manage different kinds of data, ranging from numerical, categorical or mixed data to more complex data structures, such as interval-valued, fuzzy-valued or functional data, together with some robust methods. Furthermore, the case of two-mode clustering is illustrated in a fuzzy setting.

- when: 8 February 2024, at 11.30

- where: room 206, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link video

Abstract: Calibration of option pricing models to the implied volatility surface is a complicated, yet fundamental task in the quantitative finance community. By exploiting Sequential Monte Carlo (SMC) methods we turn the standard calibration problem into a Bayesian estimation task. In this way we can construct a sequence of distributions from the prior to the posterior which allows to compute any statistic of the estimated parameters, to overcome the strong dependence on the starting point and to avoid troublesome local minima; all of which are typical plagues of the standard calibration. To highlight the strength of our approach we consider the calibration of the double jump stochastic volatility model of Duffie et. al (2000) both on simulated and real option data. From the results on both single dates and time series of implied volatilities we find that our Bayesian approach largely outperforms the benchmark in terms of run time-accuracy, option pricing errors and statistical fit. Finally, we show how to further speed up computations by leveraging delayed-acceptance MCMC methods and deep learning. This is a joint work with R. Brignone, S. Knaust and E. Lutkebohmert, University of Friburg. 

- when: 6 February 2024, at 14.00

- where: room 206, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer

Abstract: The talk will deal with the key challenge of creating prediction bands for a new observation in the functional data framework given a training set of observed functional data and possibly in presence of covariates, either scalar, categorical, or functional. Starting from the investigation of the literature concerning this topic, we propose an innovative approach building on top of Conformal Prediction and Functional Data Analysis able to overcome the main drawbacks associated to the existing approaches. Under minimal distributional assumptions (i.e., exchangeability of the random functions), we will show how the new proposed nonparametric method (i) is able to provide prediction regions which could visualized in the form of bands, (ii) is guaranteed with exact coverage probability also for finite sample sizes, and finally (iii) is computational efficient. Different specifications of the method will be compared in terms of efficiency in some simulated and real case scenarios also in the case of multi-dimensional domain and/or codomain.

- when: 22 November 2023, at 16.00

- where: room 206, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Video

Abstract:   This work analyzes how ESG ratings are aligned with climate risk as determined through various carbon indicators. In addition, the paper analyzes the effect of the level of sustainability and climate risk on the flows of funds and performance before and after the pandemic. The results show that there is an alignment between sustainability and climate change indicators when using the environmental pillar. Furthermore, it is found that the relationship between the level of sustainability, carbon indicators and investment flows is conditioned by the economic context, for example in the case of profitability. Our results lend support to the observation that investors invest in sustainability generally expecting higher returns and when these expectations are not met, they are willing to invest in unsustainable funds, with pecuniary motives predominating over non-pecuniary ones. 

when: 20 July 2023, at 11.45

where: room 103, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide 

Abstract:  An important task in regression analysis is to choose the right specification of the link function that models the dependence structure between the random elements. A challenge arises in the framework of scalar on function regression as the link function is a real-valued operator acting on a functional space, and it is difficult to visualize and hence select a coherent specification. A specification test that uses a semi-parametric approach is proposed, in particular by exploiting the Single Functional Index Model. The test statistic is a special form of U-statistic; its asymptotic null distribution is derived under suitable assumptions, and consistency is proved for a specific class of alternatives. The finite sample performances of the test are evaluated through a simulation study using both asymptotic p-values and some bootstrap approaches. An application of the method developed to a problem commonly arises in the food industry is performed to demonstrate the potentialities of the method.

when: 4 Luglio 2023, at 11.00

where: room 101, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Video

Abstract: The idea of this paper is to investigate differences in brown and green bonds from the lens of the trading activity. Our research exploits the idea that positive and negative jumps in the dynamics of returns have a specific memory nature that can be modelled through a self-exciting process. We investigate the microscopic structure and properties of high-frequency series of green and brown bonds using Hawkes type processes where the kernel is a CARMA(p,q) model. Empirical results suggest that the bid-ask spread of green bonds on average is larger for bonds issued by a financial institution while the opposite happens for bonds issued by a non financial company. Moreover, we observe that the intensities respectively of positive and negative jumps in the price dynamics are not stationary through time. Higher order bivariate Hawkes models provide better fitting results in our datasets, especially for the issuer that operates in the energy sector.  This presentation is based on a joint work with Lorenzo Mercuri (University of Milan) and Andrea Perchiazzo (Vrije Universiteit Brussel).

when: 14 June 2023, at 11.00

where: room 101, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide

Abstract: Classical inference in statistics is typically carried out by means of standard (first-order) asymptotic theory. However, the asymptotic distribution of estimators and test statistics can provide a poor approximation of tail areas especially when the sample size is moderate to small. This can lead to inaccurate p-values and confidence intervals.
Several techniques, both parametric and nonparametric, have been devised to improve first-order asymptotic approximations, including e.g. Edgeworth expansions, Bartlett's corrections, and bootstrap methods. Here we focus on saddlepoint techniques, introduced into statistics by H. Daniels, and more generally on small sample asymptotic techniques, an expression coined by F. Hampel to express the spirit of these methods. Indeed they provide very accurate approximations of tail probabilities down to small sample sizes and /or out in the tails. Moreover, these approximations exhibit a relative error of order 1/n, an improvement with respect to other available approximations obtained by means of Edgeworth expansions and similar techniques.
We will review the basic ideas, show the link with other nonparametric methods such as empirical likelihood, and outline some connections to information theory and optimal transportation.

when: 31 January 2023, at 16.30

where: room 101, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide Link Video

Abstract: Over recent years, text modeling techniques have been employed in several applications, including the detection of latent topics in text documents. A widespread statistical tool for topic modeling is the Latent Dirichlet Allocation (LDA), which allows for a document representation in terms of topic composition. A well-known limitation of the LDA is related to the stiffness of the Dirichlet prior imposed on the topic distributions. To consider a richer dependence structure, we propose a generalization of the Dirichlet distribution as an alternative distribution, namely the flexible Dirichlet (FD). The FD is a distribution defined on the simplex space allowing for a finite mixture structure. This choice introduces additional parameters in the LDA, and ensures more flexibility, still maintaining the model interpretability, as well as conjugacy to the multinomial model. The latter property allows for a Collapsed Gibbs Sampling-based estimation procedure. The generalization of the LDA based on the FD distribution is illustrated via an application to a real dataset.

when: 14 December 2022, at 16.00

where: room 203, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide Link Video

Abstract: We model sovereign debt sustainability with optimal financing decisions under macroeconomic, financial, and fiscal uncertainty, with endogenous risk and term premia. Using a coherent risk measure we trade off debt stock and flow risks subject to sustainability constraints. We optimize static and dynamic financing strategies and demonstrate economically significant savings from optimal financing compared with simple rules and consols, and find that optimizing the trade-offs can be critical for sustainability.

when: 6 December 2022, at 16.00

where: room 101, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide Link Video

Abstract: In this talk, we present a new framework of additive regression modelling for data in very generic settings. More precisely, we tackle the problem of estimating component functions of additive models where the regressors and/ or response variable belong to general Hilbert spaces and can be imperfectly observed. By this, we mean that some variables can be either measured incompletely or with errors. Smooth backfitting methods are used to estimate consistently the component functions and we provide explicit rates of convergence. We amply illustrate our methodology in various settings, including the functional, Riemannian and Hilbertian settings.

when: 8 November 2022, at 16.00

where: room 201, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.

Link Flyer Link Slide Link Video