Dear colleagues,

you are all invited to participate in the following seminar organized by QFinLab – Department of Mathematics, Politecnico di Milano.

Wednesday, 5 March 2025, 12.00-13.00

Seminar room, third floor, building 14, Via Bonardi 9, Milano (Leonardo Campus)

Katia Colaneri (Università di Roma Tor Vergata)

Title: Expect the worst! Optimal emission abatement under tax policy uncertainty and stochastic differential games. 

Abstract: We study the problem of a profit maximizing electricity producer who has to pay carbon taxes and who decides on investments into technologies for the abatement of CO emissions in an environment where carbon tax policy is random and where the investment in the abatement technology is divisible, irreversible and subject to transaction costs.
We consider two approaches for modelling the randomness in taxes. First we assume a precise probabilistic model for the tax process, namely a pure jump Markov process (so-called tax risk); this leads to a stochastic control problem for the investment strategy.  
Second, we analyze the case of an uncertainty-averse producer who uses a differential game to decide on optimal production and investment. We carry out a rigorous mathematical analysis of the producer’s optimization problem and of the associated nonlinear PDEs in both cases. Numerical methods are used to study quantitative properties of the optimal investment strategy.   
We find that in the tax risk case the investment in abatement technologies is typically lower than in a benchmark scenario with deterministic taxes. However, there are a couple of interesting new twists related to production technology, divisibility of the investment, tax rebates and investor expectations. In the stochastic differential game on the other hand an increase in uncertainty might stipulate more investment.

Next seminar: Claudio Fontana (Università di Padova), 2 April 12.00.

All news can be found on the QFinLab webpage.

The organizers: Michele Azzone and Alessandro Calvia

Dear colleagues,

you are all invited to participate in the following seminar organized by QFinLab – Department of Mathematics, Politecnico di Milano.

Wednesday, 19 February 2025, 12.15-13.15

Seminar room, third floor, building 14, Via Bonardi 9, Milano (Leonardo Campus)

Marzia De Donno (Università Cattolica del Sacro Cuore)

Title: Short rate models with stochastic discontinuities: a PDE approach.

Abstract: With the recent reform of interest rate benchmarks, interbank offered rates (IBORs) like LIBOR have been replaced by risk-free rates (RFRs), such as the Secured Overnight Financing Rate (SOFR) in the U.S. and the Euro Short-Term Rate (€STR) in Europe. These rates exhibit characteristics like jumps and spikes that correspond to specific market events, driven by regulatory and liquidity constraints. To capture these characteristics, this paper considers a general short-rate model that incorporates discontinuities at fixed times with random sizes. Within this framework, we introduce a PDE-based approach for pricing interest rate derivatives. For affine models, we derive (quasi) closed-form solutions, while for the general case, we develop numerical methods to solve the resulting PDEs.

(Joint work with A. Calvia, C. Guardasoni, S. Sanfelici).

Next seminar: Katia Colaneri (Università di Roma Tor Vergata), 5 March 12.00.

All news can be found on the QFinLab webpage.

The organizers: Michele Azzone and Alessandro Calvia

January 16, 2025

15.00-17.00

Department of Mathematics- Saleri room- VI floor

Tiziano De Angelis (Università di Torino)

A model of strategic sustainable investment

We study a problem of optimal irreversible investment and emission reduction formulated as a nonzero-sum dynamic game between an investor with environmental preferences and a firm. The game is set in continuous time on an infinite-time horizon. The firm generates profits with a stochastic dynamics and may spend part of its revenues towards emission reduction (e.g., renovating the infrastructure). The firm’s objective is to maximize the discounted expectation of a function of its profits. The investor participates in the profits and may decide to invest to support the firm’s production capacity. The investor uses a profit function which accounts for both financial and environmental factors. Nash equilibria of the game are obtained via a system of variational inequalities. We formulate a general verification theorem for this system in a diffusive setup and construct an explicit solution in the zero-noise limit. Our explicit results and numerical approximations show that both the investor’s and the firm’s optimal actions are triggered by moving boundaries that increase with the total amount of emission abatement.

Joint work with C.C. Rodrigues Graciani (Scuola Superiore Meridionale) and P. Tankov (ENSAE)

Discussant: Alessandro Calvia (Politecnico di Milano)

Sandra Paterlini (Università di Trento)

Chasing ESG performance: How Methodologies Shape Outcomes

ESG metrics play a crucial role in sustainable finance but face growing criticism for their inability to accurately capture true sustainability improvements. This study investigates how methodological choices can introduce distortions in ESG scores, with a primary focus on Refinitiv ESG data, while offering insights applicable to other providers as well. We show that methodological choices, such as score normalization, significantly impact the ability of scores to reflect genuine sustainability progress. Specifically, the inclusion of new, lower-performing entrants can artificially inflate the scores of top-ranked companies, obscuring actual improvements by relying on peer comparisons. Moreover, our analysis reveals that once companies achieve an A-rating category, they are unlikely to be downgraded, further highlighting the impact of these methodological decisions on the dynamics of ESG scoring. Analyzing data from three key sectors over the period 2012–2021 reveals that less than 45% of total score variation is attributable to company disclosures, underscoring the influence of score construction methodologies. By constructing a much simpler aggregation method, we demonstrate strong correlation with Refinitiv’s scores while reducing distortions from new entrants and peer effects, offering a more transparent and representative measure of sustainability performance.

Joint work with Matteo Benuzzi, Karoline Bax and Emanuele Taufer

Discussant: Michele Azzone (Politecnico di Milano)

This event has been partially supported by MUR, Department of Excellence 2023-27 

QFinLab promotes a series of thematic seminars on climate risk. Climate transformations have a deep impact on economic activity with implications ranging from the definition of green transition policies to the evaluation of financial assets, from the construction of innovative financial and insurance products to risk management, from the design of mechanisms incentive to asset management and much more. Themes that pose intriguing questions to the academic world, involving in particular, those who deal with models to interpret a phenomenon that by its nature is very complex. The activities are organized through a series of double seminars with discussants. The first meeting is scheduled for

November 21, 2024

14.30-16.30

Department of Mathematics
Saleri room- VI floor

• Emanuele Campiglio (Università di Bologna) Optimal Climate Policy as If the Transition Matters
  Discussant: Aldo Nassigh (Politecnico di Milano)
• Enrico Biffis (Imperial College Business School) Short-lived Gasses, Carbon Markets and Climate Risk Mitigation
  Discussant: Edit Rroji (Università degli Studi di Milano Bicocca)

Next meetings: 16 January, 2025: Tiziano De Angelis (Università di Torino), Sandra Paterlini (Università di Trento); 20 March, 2025: Andrea Macrina (UCL), Luca Regis (Università di Torino)

This event has been partially supported by MUR, Department of Excellence 2023-27