Abstract: Agricultural natural disasters have become a key factor that influences the incomes of a tremendous number of small farmers. An effective lever, agricultural insurance, thus emerges to deal with the natural disasters. Insurance companies have successfully promoted and implemented such insurance types as output insurance and weather index insurance. Output insurance is one of the most common kinds of insurance in the market. The insured takes the output of the crops planted by the insured as the insured object and the insurer pays compensation according to the loss value of the actual output of the insured which is lower than the insured output, while weather index insurance is the innovation of agricultural insurance, which can meet the farmers’ security demand and effectively protect the farmers’ interests. This insurance refers to the insurance mechanism that takes weather index as the trigger condition. When the trigger condition is reached, the insurance company will pay insurance benefits to the insured according to the weather index regardless of whether the insured is affected by the disaster. The existing literature has not considered the use of agricultural insurance to transfer uncertain risks, and the literature of agricultural insurance has only considered the impact of single insurance mechanism. However, various kinds of agricultural insurance in practice bring farmers trouble in the choice. Therefore, from the perspective of farmers, considering how farmers with risk aversion transfer the natural disaster risk in the production process through agricultural insurance when weather conditions and effort level jointly affect output, this paper analyzes how farmers make insurance participation decisions and insurance choices, as well as the impact of different insurance mechanisms on farmers’ production decisions.
This paper employs the conditional value-at-risk(CVaR)risk measurement criterion to characterize farmers’ risk aversion and builds a Stackelberg game model between risk aversion farmers and risk-neutral insurance companies. Considering the fact that the weather conditions and the effort level of farmers’ production inputs together affect the output, we first study the farmers’ optimal effort level decision and its utility under different agricultural natural disaster insurance and the insurance company’s optimal compensation decision and expected income, and in turn, we discuss and analyze the influence of the degree of risk aversion on the optimal decisions and utility/income of both sides. Second, we compare the difference between the optimal decision and utility/expected income of both sides under output insurance and weather index insurance, so that they know how to choose agricultural natural disaster insurance. Finally, through numerical analysis, we find the effects of the degree of risk aversion, insurance output and weather index on farmer’s utility, insurance company’s expected output and insurance type selection.
The main results suggest that: (i)Output insurance will restrain the effort level of farmers’ production inputs, while weather index insurance can encourage farmers to improve their effort level and thereby increase agricultural product supply. The utility of farmers under weather index insurance, however, is not necessarily higher than that under output insurance. (ii)Whether farmers adopt insurance strongly depends on the degree of risk aversion. Specifically, only if the risk aversion is salient, the farmers would adopt agricultural natural disaster insurance. Furthermore, their optimal insurance choices will be changed from output insurance to weather index insurance as the risk aversion degree increases, which is also confirmed by numerical analysis.
Our model has several management implications. First, when the degree of risk aversion is low, participating in production insurance can better cope with natural disasters, but when the degree of risk aversion is high, participating in weather index insurance can obtain higher risk returns. Second, for farmers with low risk aversion, it is a better choice for insurance companies to provide output insurance. For farmers with a high degree of risk aversion, insurance companies are more willing to provide weather index insurance for them, which may achieve a win-win situation for both sides.

Key words: output insurance, weather index insurance, insurance decision, insurance choice, CVaR

摘要： 农业自然灾害是影响我国众多小农户收入的重要因素,而农业保险是应对自然灾害的有效手段。本文运用条件风险估值(Conditional Value-at-Risk,CVaR)风险度量准则刻画农户的风险规避特性,构建风险规避农户和风险中性保险公司之间的Stackelberg博弈模型,对比分析了产量保险和气象指数保险机制下农户和保险公司的最优决策行为以及双方的险种选择。研究发现:(1)产量保险会抑制农户生产投入的努力水平,气象指数保险却能激励农户提升努力水平进而增加市场中农产品的供应量,但是气象指数保险下农户的效用并不一定优于产量保险。(2)农户的风险规避程度是影响其是否参保的关键因素——风险规避程度较高的农户才会选择投保农业自然灾害保险,而且随着农户风险规避程度的增加其最优险种选择将由产量保险转为气象指数保险。数值分析也进一步证实了上述结论。

关键词: 产量保险, 气象指数保险, 参保决策, 险种选择, CVaR