The corresponding author is indicated by *.
Preprints
Estimating Likelihoods for NGFS Transition Scenarios with Bootstrap Confidence Intervals
Fangyuan Zhang
Link: Preprint version
Abstract: Climate scenario is a fundamental tool for studying the interaction of economic activity, transition policy and climate change. A set of scenarios , often narrative-based, describe a range of possible future transition pathways. However, the narrative nature makes it challenging to quantify the uncertainty and examine the relative likelihood of different scenarios. In this work, we propose a framework to estimate the relative likelihood of a given set of transition scenarios. Using scenario data, we define a single quantitative metric that captures the inherent decarbonization speed associated with each scenario. Thus, the original high-dimension scenario space is reduced to one interpretable dimension. Based on the ordering of scenarios on this dimension, we derive a relative probability distribution of the scenarios. Given the limited number of available scenarios, we apply a bootstrap method to construct confidence intervals for our estimates. Our numerical results show that incorporating decarbonization speeds into likelihood estimation yields more informative expectations for scenario variables than naive empirical averaging.
Climate Scenarios with Probabilities via Maximum Entropy and Indirect Elicitation
Riccardo Rebonato*, Lionel Melin and Fangyuan Zhang
Link: Preprint version
Abstract: This work proposes a framework to estimate the likelihoods of abatement scenarios. We define a quantitative metric that measures the abatement speed of a transition scenario. In particular, a one-to-one functional relationship between social-cost-of-carbon (SCC) and the abatement speed is established. By eliciting an empirical distribution of SCC from the literature, we construct the unconditional distribution of abatement speeds, thus the unconditional distribution of transition scenarios. We find that the probability of the temperature anomaly surpassing 3 degrees Celsius by 2100 is non-negligible. This suggests that the disconnect between economists' recommendations and policy action should be substantially reduced.
Journal articles
Do Transition Costs or Physical Damages Impact Equity Evaluation More?
The Journal of Portfolio Management, 2025
Riccardo Rebonato*, Lionel Melin and Fangyuan Zhang
Abstract: We look at the relative impact of climate physical damages and transition costs in the valuation of a well-diversified global equity index. The transition costs are proxied by the mitigation costs obtained from a standard integrated assessment model. Contrary to common assumptions and practices, we find that the impact of climate physical damages on equity valuation is of the same order of magnitude as that of transition costs, and can be even greater.
Non-Concave Portfolio Optimization with Average Value-at-Risk.
Mathematics and Financial Economics, 2023.
Fangyuan Zhang*
Link: Journal page / Journal version / Preprint version
Abstract: This work studies the optimal asset allocation strategy for a financial company maximizing its equity holders' utility under the average Value-at-Risk constraint. Closed-form solutions are provided in a complete financial market. We find that the company takes different strategies depending on its budget and the average Value-at-Risk constraint. In particular, different investment strategies imply different default probabilities. When the company has a low initial asset, the risk constraint has poor protection for debt holders.
Intergenerational Risk Sharing in a Defined-Contribution Pension System: Analysis with Bayesian Optimization.
ASTIN Bulletin: The Journal of the IAA , 2023
An Chen, Motonobu Kanagawa and Fangyuan Zhang*.
Link: Journal Page/ Preprint
Abstract: A defined contribution pension system has obvious advantages, such as sustainability, transparency, portability, etc. However, it cannot naturally incorporate intergenerational risk sharing, which can potentially enhance society's welfare. We consider a model with forty overlapping generations. Intergenerational risk sharing is achieved to balance the overall pension fund's stability and each generation's welfare. Using a popular machine learning approach, we conduct a comprehensive and efficient simulation study. Analysis and numerical results show that Intergenerational risk sharing can enhance each generation's welfare in a turbulent market.
On the Equivalence Between Value-at-Risk and Expected Shortfall in Non-Concave Optimization
An Chen, Mitja Stadje and Fangyuan Zhang*.
Insurance: Mathematics and Economics, 2024
Link: Preprint
Abstract: This work provides a comprehensive review of optimal asset allocation strategies under various risk constraints. If the company's target function is to maximize the utility of total assets, the problem corresponds to a constrained concave optimization problem, while it becomes constrained non-concave optimization if the company aims to maximize the utility of equity holders. One important finding is that, if the company only cares about equity holders' benefit, popular risk constraints, Value at risk or Expected shortfall, lead to the same investment strategy. The equivalence does not hold if the company cares about both equity and debt holders.