Dear colleagues,

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

Thursday, 5 June 2025, 12.15-13.15

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

Olimpia Carradori (University of Zurich)

Title:  Insurers’ carbon underwriting policies

Abstract: Insurance companies can influence the net-zero transition by limiting coverage for carbon-intensive projects. We study the adoption, structure, and effects of carbon underwriting policies among the world’s largest insurance groups. Using novel mine-level insurance data, we show that insurers with coal policies reduce the number of insured mines by approximately 16%, insured coal volumes by 56%, and make continued coverage significantly less likely. Implementation is often incomplete, and some insurers expand coverage despite commitments. Affected mines tend to reduce output, cut the number of employees, and are more likely to be idled in subsequent periods. 

Next seminars: Marco Tolotti (Università Ca’ Foscari Venezia), 9 June 12.15.

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, 7 May 2025, 12.15-13.15

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

Alessandro Sbuelz (Università Cattolica del Sacro Cuore) 

Title: The Zero-Theta Hedge Contract.

Abstract: We examine long-dated asset valuation under systematic and idiosyncratic risk, driven by extreme trajectories. By introducing the zero-Theta hedge contract, a negative-Delta derivative security with a maturity-independent price, we study investor attitudes toward systematic long-run crashes. Declining expected payoff with maturity signal strong crash aversion. The contract aids in decomposing the stochastic discount factor, shedding light on long-run crash risk premia. Even for volatile assets whose price comes from idiosyncratic rallies, systematic long-run crashes remain central to long-run risk valuation.

Based on a joint work with Anna Battauz and Marzia De Donno.

Next seminars: Olimpia Carradori (University of Zurich), 5 June. Marco Tolotti (Università Ca’ Foscari Venezia), 9 June 12.15.

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, 2 April 2025, 12.15-13.15

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

Claudio Fontana (Università di Padova)

A stochastic Gordon-Loeb model for optimal security investment under clustered cyber-attacks.

Abstract: We propose a continuous-time extension of the Gordon-Loeb model for optimal investment in information security under the threat of cyber-attacks. The arrival of attacks is modeled using Hawkes processes, capturing the realistic feature of clustering in cyber-attacks. Each attack may lead to a system breach, with the probability of breach depending on the system’s vulnerability. We aim at determining the optimal investment in cyber-security to reduce the system’s vulnerability. The problem is formulated as a two-dimensional Markovian stochastic control problem and solved via dynamic programming techniques. We perform a numerical study of the value function and the associated optimal investment strategy in cyber-security, highlighting the impact of randomly arriving clustered cyber-attacks.

Based on a joint work with G. Callegaro, C. Hillairet, B. Ongarato.

Next seminar: Alessandro Sbuelz (Università Cattolica del Sacro Cuore), 7 April 12.15.

All news can be found on the QFinLab webpage.

The organizers: Michele Azzone and Alessandro Calvia

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, 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 third meeting is scheduled for

March 20, 2025

15.00-17.00

Department of Mathematics- Seminar room- III floor

Andrea Macrina (UCL-London)

Climate-Contingent Convertible Bonds (CloCo) – Seizing the Opportunity to Innovate and Adapt

Adjustments to governmental climate transition policies and uncertainties linked to the ability for industry sectors and consumers to manufacture and purchase low carbon technologies, respectively, have led to an increasing need to embed a richer framework for uncertainty in climate transition outcomes. Such uncertainties create financial risks for firms, their investors, the banking sector, and potentially sovereign risks. The need thus arises for the development of a bespoke pricing setup and financial instruments, which offer a mechanism to share climate transition risk. As an example, we propose the so-called climate-contingent convertible (CLoCo) bond. This instrument enables firms to reduce the risk of default due to adverse climate transition policies over the product’s lifetime and to respond to new investment opportunities by freeing up capital supporting more financial agility. The proposed financial innovation implies reduced risk of default for firms, thereby increasing the expected

firm value, but it also reduces the dependency of firm failures on the banking sector and potential bail-out costs incurred by sovereign nations.

Joint work with C. Cormack

Discussant: Emilio Barucci (Politecnico di Milano)

Luca Regis (Università di Torino)

Coordinating Dividend Taxes and Capital Regulation

We study the impact of state-contingent dividend taxes (and bans) and capital regulation on a firm’s optimal strategy and value. In the model, the firm generates stochastic income under time-varying macroeconomic conditions. Its manager distributes dividends and issues costly equity to maximize shareholder value. We solve the manager’s stochastic control problem and derive the firm’s reserve distribution in closed form. Imposing dividend taxes (or bans) during crises generates a trade-off, as it encourages reserve accumulation in bad states but promotes payouts in good ones. Also, the policy undermines financial stability by reducing the firm’s value and its recapitalization incentives across states. Coordinating dividend taxes with counter-cyclical capital regulation can mitigate value losses and ameliorate the trade-off, but it also creates additional recapitalization disincentives.

Joint work with Salvatore Federico and Andrea Modena

Discussant: Alessandro Calvia (Politecnico di Milano)

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

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