Certain commodity producers face uncertain output and price, but can trade financial derivatives on price. I consider how best to use a put option on price. I introduce the variance surface, which is a data visualization technique that shows the level of variance across a grid of values for the...

Tail hedging is a portfolio management strategy meant to reduce the risk of large losses. For an investor who holds a stock market index fund, the strategy entails buying out of the money put options on the index. Research suggests the strategy works well in practice and I explore the returns to...

The existence proof of general equilibrium, which is based on subjective-behavioral axioms, is replaced by the existence proof of a final turning point, which is based on objective-structural axioms. The final turning point is characterized by an irreversible switch from profits to losses for...

In a recent article, Keen resumes the debate with Krugman about the effects of debt upon the economy. It is hard to see how the question can be settled as long as all participants apply their idiosyncratic models. Hence the issue boils down, as Krugman rightly put it, to the deeper question:...

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of...