We are interested in pricing rainfall options written on precipitation at specific locations. We assume the existence of a tradeable financial instrument in the market whose price process is affected by the quantity of rainfall. We then construct a suitable 'Markovian gamma' model for the rainfall process which accounts for the seasonal change of precipitation and show how maximum likelihood estimators can be obtained for its parameters. We derive optimal strategies for exponential utility from terminal wealth and determine the utility indifference price of the claim. The method is illustrated with actual measured data on rainfall from a location in Kenya and spot prices of Kenyan electricity companies.Rainfall derivatives, Seasonality, Discrete-time Markov control process, Utility indifference pricing, Monte Carlo methods,
Since the inception of the novel Corona Virus Disease-19 in December in China, the spread has been massive leading World Health Organization to declare it a world pandemic. While epicenter of COVID-19 was Wuhan city in China mainland, Italy has been affected most due to the high number of recorded deaths as at 21st April, 2020 at the same time USA recording the highest number of virus reported cases. In addition, the spread has been experienced in many developing African countries including Kenya. The Kenyan government need to make necessary plans for those who have tested positive through self-quarantine beds at Mbagathi Hospital as a way of containing the spread of the virus. In addition, lack of a proper mathematical model that can be used to model and predict the spread of COVID-19 for adequate response security has been one of the main concerns for the government. Many mathematical models have been proposed for proper modeling and forecasting, but this paper will focus on using a generalized linear regression that can detect linear relationship between the risk factors. The paper intents to model and forecast the confirmed COVID-19 cases in Kenya as a Compound Poisson regression process where the parameter follows a generalized linear regression that is influenced by the number of daily contact persons and daily flights with the already confirmed cases of the virus. Ultimately, this paper would assist the government in proper resource allocation to deal with pandemic in terms of available of bed capacities, public awareness campaigns and virus testing kits not only in the virus hotbed within Nairobi capital city but also in the other 47 Kenyan counties.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.