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We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution, specially when extreme situations occur (pandemics, global wars, etc.). When, between jumps, the dynamical evolution is governed by an Ornstein–Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continuous time random walk.

In the agricultural sector, risks are inherent and ubiquitous, posing potentially serious consequences for stakeholders and consumers. Risks disrupt supply chains, causing extensive financial and economic losses. Agricultural risks are also the principal cause of transient food insecurity, creating a poverty trap for millions of households across the developing world that enforces a vicious cycle of shock and recovery. Climate change is exacerbating this cycle by shifting the frequency and intensity of weather related risks and increasing uncertainty. Effective agricultural risk management (ARM) is crucial to increasing economic growth, improving food security, and reducing poverty. Although levels of risk vary within and between countries, lower-income and highly agriculture-dependent countries are more vulnerable to agriculture-related risks. In these countries, there is an urgent need to better assess risks, understand the interconnections between different types of risk, and improve agricultural risk management strategies.

At the request of the government of Kenya and under its guidance, a team of national and international experts conducted an appraisal of different agricultural insurance options for Kenya.This appraisal, as set out in this document and the accompanying technical analysis, lays out the costs and benefits of developing large-scale agricultural insurance that involves both the public and private spheres.The analysis considers potential structures for large-scale agricultural insurance in Kenya, the fiscal cost to the government of Kenya, and the economic benefits for farmers and pastoralists.In order for it to partner with the private sector to prepare and implement a large scale agricultural insurance program, the government should consider taking the following next steps.The government of Kenya may build on there commendations by the Program Steering Committee to take the lead in formulating a national policy on agriculture insurance, in cooperation with county administrations and private insurance companies. The government of Kenya may develop a road map for establishing the institutions required for large-scale agricultural insurance programs, with the goal of covering at least a fifth of Kenya’s agricultural producers. As next steps for establishing livestock insurance, the government of Kenya may decide how to integrate the proposed insurance product with other existing protection mechanisms. As next steps for crop insurance, the government of Kenya may seek consultations with agricultural banks and work with private sector insurers to develop a data audit system acceptable to international reinsurers.