Catastrophe risk bonds are always within a multi-asset class portfolio of alternative risk premia in many hedge funds. In this paper, we consider an over-the-counter insurance contract on catastrophe risk between an insurance company and a hedge-fund. The contract acts as a bond within which the insurance company, which issues the bond, pays payments higher than the market risk-free interest, in order to be insured against the risk of a predefined natural catastrophe. The contract is priced by the utility indifference pricing method. We apply our framework to price agricultural catastrophe bonds in two cities in Iran where their harvests are exposed to the risk of low temperature.

In this article, we introduce price index insurances on agricultural goods. Although these seem similar to derivatives, there are significant differences between price index insurances and derivatives. First, unlike derivatives, there are no entrance barriers for purchasing insurances, making them the risk management tools that are accessible to almost all farmers. Second, since insurances are issued in a certain number for any individual farm, unlike futures, for example, they cannot be used for speculation and are used solely for hedging price risk. Third, unlike forwards, they are heavily regulated and do not default and cause counterparty risk. In addition to all differences (or benefits), such products have just recently been introduced in the agricultural insurance market. In this article, we investigate if there could have been a financially viable market where these products are traded. More precisely, we investigate whether an insurance company can design a portfolio of optimal contracts that gives a higher Sharpe ratio than the financial market index prices (here, FTSE 100 and other three major indexes). To reach the article’s objective, we take three steps, in considering theoretical, practical, and corporation standpoints. In the first step, we show what an optimal contract would look like from the demand side in a theoretical setup and we obtain the optimal contract from the farmers' standpoint. In the second step, by adopting a more practical approach in meeting the Key Performance Indicators requirements set by the market participants (both demand and supply side), we find the optimal policies specifications from the first step, in the market equilibrium. This step also helps to determine some unobservable market parameters like volatility. Finally, by adopting a corporation standpoint we bring our model to the U.K. farm index prices and find an optimal portfolio of the products on products from 10 commodities. We demonstrate that investing in such a business is financially viable, as the optimal insurance portfolio produces a Sharpe ratio that outperforms the FTSE 100 and other major market indexes.

The main objective of this article is to model the losses caused by frost events and use it to price frost insurance. Since the data on frost events are either unavailable or rarely available, we have chosen to obtain a model for frost losses based on temperature by using some fundamental agricultural engineering findings on frost damage. The main challenges in modeling frost loss variables are, first, the nonlinearity of the frost losses with respect to the temperature and, second, the fruit resistance to the first few hours of low temperature. We address both issues when introducing our frost loss variable. Then after finding the loss model, we use it to price frost insurance for a general family of insurance contracts that do not generate any risk of moral hazard. In particular, we will find the premiums of stop-loss policies for losses to citrus fruits using Value at Risk, Conditional Value at Risk, and Wang's premium based on temperature data from San Joaquin Drainage in California.

In this paper, we study the structure of optimal contracts in banking system when there is no risk of moral hazard. We consider a risk management problem under a policy that reduces the excessive risk-taking behavior by making all banks bear part of the risk that they transfer to other parties in the market. First, we characterize the optimal solutions to the risk management problem, and, second, we find a necessary and sufficient condition under which the “risk of the tail events” will not be transferred. In particular, we will study the problem using two known risk measures, value at risk and conditional value at risk, and will show that in these cases, the optimal solutions are in the form of stop-loss policies.

In this paper we introduce a new coherent cumulative risk measure on a subclass in the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed.