Optimal Agricultural Yield Insurance And Subsidy Design Under Farmer's Willingness Yield

Agricultural production practices have been long emphasized by many governments due to its overriding importance on food security and social well-being to almost every nation.Particularly to us China,this meaning needs not to be doubted.As the most widely used meaning of actively managing agricultural production,yield insurance has always been playing its important role on deviating production risk and help keep sustainability.Unlike other risky practices,agricultural production has very strong externality,which often triggers market failure,thus requiring more careful design in indemnity by management authorities.In the process of yield insurance design,the prior issue is to design its indemnity.In practices,traditional individual yield insurance often has greater operational cost and much more severe moral hazard problem,whereas index yield insurance poses no moral hazard,but with more basis risk,which would potentially undermines its uses.Based on these perspectives,we put much effort on designing a new indemnity function form,which simultaneously has the merit of index yield insurance,while eliminating the moral hazard problem,thus indeed is a fairly effective tool.On the view of stimulating farmers' production willingness,how yield insurance would influence farmers' behaviors is indeed a more important issue that needs to be thoroughly considered.If a certain yield insurance product provides farmer with yield protection,but in cost of lowering their production willingness,it is clearly not a consequence that we want to see.For this reason,the design in agricultural yield insurance not only needs to consider the side of risk mitigation,but also needs to consider the stimulation towards farmers' production practices.In this case,we implement a solid and integrated modelling framework to analyze the impacts of different insurance types towards farmers' production decisions.And we find that,yield insurance may not do good in stimulating farmers to produce more,on the contrary,it may lowers farmers production willingness.The conclusion has great importance,as it could be used as accordance in yield insurance design practices.This thesis is comprised of eight chapters.Chapter 1 is introduction.Chapter 2 is the basics of Miranda Decomposition and its further generalization.Chapter 3 provides some simple but meaningful insights on explaining how yield insurance would impact farmers' behavior by assuming some extreme scenarios.Chapter 4 provides the forms of optimal index yield insurance indemnity design under expected utility maximization of farmers' terminal wealth.Chapter 5 gives a thorough analysis on the effect caused by different yield indemnity designs on farmer's willingness yield under exponential and quadratic utility assumption.Chapter 6 examines the effectiveness of premium subsidy under two utility scenarios.Chapter 7 gives some more detailed discussions on SQP and PERT fitting techniques that have been used in earlier chapters.Chapter 8 concludes the thesis and come up with some future directions.In chapter 1,we give some background introduction on the topics of methods,research meanings,difficulties and so forth.We give a brief look at our research topics,and pose some literature reviews mainly focusing on yield decomposition,yield insurance form and farmers' dynamic behaviours.In chapter 2,we firstly quote the so called classic Miranda model and prove some of its mathematical properties based on the yield insurance framework.Besides,we implement the "degree of variance deviation" as a quantitative tool to analyze risk coverage property Miranda model poses in individual,area and no insurance cases.Moreover,we generalize Miranda model by redefine its original "exogenous yield mean" to "indogeneous willingness yield" and give a new explanation on the relationship between farmers' behaviors and their yields.In chapter 3,we define three different scenarios based on Miranda model,namely,individual yield insurance,index yield insurance and no insurance cases.We derive some results mainly on the perspective of farmers' optimal willingness yield under maximum return ratio and maximum net income objectives.Based on the quantities of those value functions,we compare the choices farmers would make under every scenarios.Indeed,we don't consider the impact of utility,while assuming some extreme conditions,thus making our results more ore less not robust.But they still pose some meaningful instincts.In chapter 4,we use maximum expected utility of terminal wealth as the objective and consider the following optimal index yield insurance indemnity problems under five commonly used premium principle constraints.Through convex analysis,we prove that these optimization problems are all strict convex ones and have unique global solutions.Moreover,we show that the solutions would be taken on the boundary of each inequality constraint and use Lagrange and KKT method to generate some difference and ordinary differential equations with respect to optimal indemnities that are equivalent to the primal optimization problems.Our results significantly widen the range of existed literatures and generalize the results of Zhang,Tan,et.al.,2019.Besides,the method we use is of greater universality and simplicity.In chapter 5,we further generalize the modeling framework to those implemented in chaplet4,so that they could also be used to analyze the corresponding individual yield insurance indemnity problems.In particular,we define a new individual yield insurance indemnity form,that is,a function with determinant of index and parameter of willingness yield.This new formulation could totally eliminate moral hazard.Through the same modeling framework,we then analyze the optimal willingness under quadratic utility and exponential utility assumptions.The results show that under both cases,index yield and individual yield indemnities are piecewise linear functions with respect to risks,while the willingness yield in individual yield insurance is neutral towards indemnities.Furthermore,under quadratic utility,farmers may or may not purchase yield insurance,whereas under exponential utility,farmers will bound not to purchase yield insurance.Besides,the willingness yield will decline under both cases,which infers the fact that yield insurance will potentially undermines farmers' motivation towards agricultural production.In chapter 6,we use the same models that have been used in earlier chapters,and add premium subsidy into them,analyze its effectiveness towards farmer's selection among individual,index and no insurance.By examining the outcomes of introducing premium subsidy to different scenarios,we find that farmers with quadratic utility would tend to purchase yield insurance,while having greater willingness yield.Whereas in the exponential utility case,farmers would not raise their willingness yields,though they still intend to purchase more yield insurance.In chapter 7,we re-elaborate some methods that have been used in earlier chapters,but without thorough discussions.To be concrete,we explain the logic of SQP algorithm that is used in generating the optimal solutions of index indemnity function in empirical model.And we implement some random experiments to examine the robustness of the so called PERT fitting technique that is often used in fitting yield distributions.Chapter 8 concludes the thesis and come up with some future research directions.