In recent years we have been witnessing an increase in extreme events, which cause significant damage to human activities, especially from an economic perspective. The present research project aims to provide quantitative tools both for the measurement and the management of two emerging risks, namely the weather risk in agriculture and the seismic risk.
The aim of the project is twofold. On the one hand, we want to provide an actuarial pricing model for the coverage of damage caused by catastrophic events, in accordance with national and international legislative provisions, also by exploiting new technologies, such as Deep Learning. On the other hand, we want to guarantee appropriate hedging strategies, by transferring the risk to the capital market, using appropriate financial instruments, whose risk-neutral price must be evaluated.
The research project aims to implement actuarial models for managing natural catastrophic risks, also considering climate changes, with a twofold purpose: we aim to conceive a fair value pricing model to reap a viable, collective insurance premium for protection system members; then, we will explore traditional and alternative mechanisms for insurance risk transfer through both traditional and financial reinsurance programs, resorting to capital market instruments.
We first focus on weather risk, in view of hedging against the implications of climate change in agriculture. Traditionally, the literature proposes either specific weather risk policies or multi-peril crop insurance, yielding indemnities often based on the subjective assessment and estimation made by the insurance firm's management. Rather, as explained in Carter et al. (2017), effective and low-cost techniques should be implemented. This means to discard self-insurance, individual insurance, or mutual insurance. Following Solvency II guidelines, we plan to build an index-based actuarial model to assess the fair premium. The reimbursement sum is linked to a synthetic index involving the agronomic specifications of the product and the type of climate event.
Moreover, since natural hazards might result in extreme losses, insurers are increasingly turning to the reinsurance market to weigh down their risk profiles, see Biffis and Chavez (2017) and Lin and Lai (2012).
However, reinsurers set the risk limits they would like to take on, making also financial markets solutions attractive: the insurance serves as an asset exchangeable with a counterparty, before paying floating coupons tied to calamity occurrence as a default event. From a financial engineering perspective, we plan to design new insurance-linked securities (ILS) as an effective vehicle for handing risk. Furthermore, we will fashion the underlying processes dynamics, exploiting analytical and/or numerical methodologies to establish the fair price of such financial products, according to the existing literature (Lin and Lai, 2012). Due to the lack of access to no-arbitrage arguments, we will employ suitable approaches to assess the market price of risk. Besides, if no closed-form pricing formulae can be obtained, we will probe ad-hoc numerical techniques, such as lattices-based methods.
A further goal of this research project is to derive the optimal reinsurance strategy between proportional and non-proportional treaties as well as the optimal parameters of the layer reinsurance. Moreover, we aim at developing a stochastic control model for designing the optimal risk allocation policy between traditional and financial reinsurance by minimizing the insurer and reinsurer total risk exposure under suitable risk measures.
Then, we center upon seismic risk. Notably, we would like to establish an actuarial pricing model for determining a fair insurance premium to cover economic earthquake damages. Formally, the premium computation requires a time-space frequency modeling, as well as the damage amount caused by severe magnitudes. As argued in Mariani et al. (2016), different time-dependent uncertainty sources might impact on seismic events for a given region; hence, modeling time series earthquakes is a suitable perspective. In a continuous-time framework we will consider high-dimensional stochastic differential equations systems, whose solutions could stem from using Artificial Intelligence models, cf. Beck et al. (2019). In particular, we refer to Deep Neural Networks, thanks to their functional approximation properties.
Earthquake insurance entails a heavy risk, whose sharing is essential. We call for seismic risk transferring solutions able to generate risk mitigation effects and lower capital charges, in a Solvency II mindset. Since reinsurance earthquake treats are not widely available, an alternative risk transfer could be guaranteed by the capital market, wherein risk sharing and diversification are profitable. However, the ILS cash-flows linked to earthquakes, as the well-known Catastrophe Bonds, cannot be hedged by a portfolio of traditional assets, so a pricing problem emerges in an incomplete market framework. Our second goal moves towards two directions. First, we will inspect fair pricing techniques compliant with the non-headgeable nature of earthquakes financial reinsurance; second, we will analyze suitable dynamic asset allocation problems to optimize the mitigation effect of financial reinsurance.