Enrico Biffis

This paper revisits the classical Merton portfolio choice problem over infinite horizon for high risk aversion, addressing technical challenges related to establishing the existence and identification of optimal strategies. Traditional methods rely on perturbation arguments and/or impose restrictive conditions, such as large discount rates and/or bounded strategies, to ensure well-posedness. Our approach leverages the problem's homogeneity to directly solve the associated Hamilton-Jacobi-Bellman equation and verify the optimality of candidate strategies without requiring transversality conditions.

Monitoring companies’ contributions to climate dynamics and their exposure to transition risks requires accurate measurements of their non-carbon dioxide greenhouse gas emissions (non-CO₂ GHG). However, carbon accounting standards are not harmonised and allow for some discretion when converting emissions of different GHGs into CO₂ equivalent units, the currency in which carbon footprints are expressed. Focusing on methane, we build counterfactual harmonised standards using the latest IPCC Global Warming Potential (GWP) values over 100 years and estimate a cumulative gap in reported methane emissions of 170MtCO₂e ( ~6Tg) over a sample of 2864 companies. Changing the counterfactual from GWP₁₀₀to GWP₂₀, as recently codified in certain jurisdictions and initiatives, increases the cumulative gap to 3300MtCO₂e ( ~40Tg). The gap only covers direct emissions and hence understates the extent of potential under-reporting across value chains. Overall, our study underscores the importance of global harmonisation of CO₂-equivalence standards to coherently track corporate GHG emissions and their exposure to transition risks.

We study an agent's lifecycle portfolio choice problem with stochastic labor income, borrowing constraints and a finite retirement date. Similarly to arXiv:2002.00201, wages evolve in a path-dependent way, but the presence of a finite retirement time leads to a novel, two-stage infinite dimensional stochastic optimal control problem with explicit optimal controls in feedback form. This is possible as we find an explicit solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, which is an infinite dimensional PDE of parabolic type. The identification of the optimal feedbacks is delicate due to the presence of time-dependent state constraints, which appear to be new in the infinite dimensional stochastic control literature. The explicit solution allows us to study the properties of optimal strategies and discuss their implications for portfolio choice. As opposed to models with Markovian dynamics, path dependency can now modulate the hedging demand arising from the implicit holding of risky assets in human capital, leading to richer asset allocation predictions consistent with wage rigidity and the agents learning about their earning potential.

We consider the valuation of contingent claims with delayed dynamics in a Samuelson complete market model. We find a pricing formula that can be decomposed into terms reflecting the current market values of the past and the future, showing how the valuation of prospective cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity. The formula we derive has successfully been used to explicitly solve the infinite dimensional stochastic control problems addressed in Biffis et al. (SIAM J Control Optim 58(4):1906–1938, 2020), Djeiche et al. (Stoch Process Appl 145:48–85, 2022) and Biagini et al. (SIAM J Financial Math 13(3):1004–1039, 2022).

We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity. The formula we derive has successfully been used to explicitly solve the infinite dimensional stochastic control problems addressed in different settings.

Technology adoption is crucial for the development of low income countries. This paper investigates how parametric insurance can contribute to improving access to finance, and hence to technology, for smallholder farmers. In a model with moral hazard, we show that bundling para-metric insurance with loans may lower collateral requirements, thus promoting the financial inclusion of poor households. The case of agricultural input loans and weather-index insurance is studied in detail and related to bundled finance solutions recently piloted among smallholder farmers in Tanzania.

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible because we are able to find an explicit solution to the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if state constraints are present. To the best of our knowledge, this is the first infinite dimensional generalization of Merton's optimal portfolio problem for which explicit solutions can be found. The explicit solution allows us to study the properties of optimal strategies and discuss their financial implications.

There is an increasing likelihood that governments of major economies will act within the next decade to reduce greenhouse gas emissions, probably by intervening in the fossil fuel markets through taxation or cap & trade mechanisms (collectively “carbon pricing”). We develop a model to capture the potential impact of carbon pricing on fossil fuel stocks, and use it to inform Bayesian portfolio construction methodologies, which are then used to create what we call Smart Carbon Portfolios. We find that investors could reduce ex-post risk by lowering the weightings of some fossil fuel stocks with corresponding higher weightings in lower-risk fossil fuel stocks and/or in the stocks of companies active in energy efficiency markets. The financial costs of such de-risking strategy are found to be statistically negligible in risk-return space. Robustness of the results is explored with alternative approaches.

The increase in frequency and severity of extreme weather events poses challenges for the agricultural sector in developing economies and for food security globally. In this article, we demonstrate how machine learning can be used to mine satellite data and identify pixel‐level optimal weather indices that can be used to inform the design of risk transfers and the quantification of the benefits of resilient production technology adoption. We implement the model to study maize production in Mozambique, and show how the approach can be used to produce countrywide risk profiles resulting from the aggregation of local, heterogeneous exposures to rainfall precipitation and excess temperature. We then develop a framework to quantify the economic gains from technology adoption by using insurance costs as the relevant metric, where insurance is broadly understood as the transfer of weather‐driven crop losses to a dedicated facility. We consider the case of irrigation in detail, estimating a reduction in insurance costs of at least 30%, which is robust to different configurations of the model. The approach offers a robust framework to understand the costs versus benefits of investment in irrigation infrastructure, but could clearly be used to explore in detail the benefits of more advanced input packages, allowing, for example, for different crop varieties, sowing dates, or fertilizers.