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The purpose of this paper is to investigate the best frequency description of a chain dependent Markov process for the daily simulation of precipitation. The influence of the order of the Markov chain model to simulate daily precipitation occurrence is evaluated. A mixed‐order model is constructed and compared to a simple first‐order model to evaluate the importance of the model order for the pricing of a rainfall index put option.

For the first time a mixed‐order Markov chain model is presented where the monthly varying order was chosen based on a Bayesian information criteria analysis of rainfall data for one weather station in the US. The outcome of this model is compared to simpler Markov models and to burn analysis results.

The comparison indicate that there is only a slightly better representation of the rain statistics in the theoretically best mixed‐order Markov chain model compared to a more simple first‐order model. Clear differences between the daily simulation and the burn method are found when pricing a put option on a rainfall index. All daily simulation models underestimate the volatility of the monthly rainfall amount especially in the summer months.

To assess the robustness and any geographical dependence of the bias in the volatility a systematic analysis could be applied to more weather stations across the US in further studies.

The bias in the volatility has significant influence on the price of the put option considered here and limits the use of such a model for risk analyses, e.g. for an extreme event cover.

For the first time a multi‐order Markov chain model is applied to price a precipitation derivative. While the focus of previous studies was the appropriate choice for the intensity process, the importance of the frequency process is investigated in this paper.

This paper aims to formalize long-term trajectories of human civilization as a scientific and ethical field of study. The long-term trajectory of human civilization can be defined as the path that human civilization takes during the entire future time period in which human civilization could continue to exist.

This paper focuses on four types of trajectories: status quo trajectories, in which human civilization persists in a state broadly similar to its current state into the distant future; catastrophe trajectories, in which one or more events cause significant harm to human civilization; technological transformation trajectories, in which radical technological breakthroughs put human civilization on a fundamentally different course; and astronomical trajectories, in which human civilization expands beyond its home planet and into the accessible portions of the cosmos.

Status quo trajectories appear unlikely to persist into the distant future, especially in light of long-term astronomical processes. Several catastrophe, technological transformation and astronomical trajectories appear possible.

Some current actions may be able to affect the long-term trajectory. Whether these actions should be pursued depends on a mix of empirical and ethical factors. For some ethical frameworks, these actions may be especially important to pursue.