Ambiguity and the language of long run risk

[Antony Millner]

Dear Colleagues,

On the advice of my friend Marcus Pivato, I am writing to share a draft of a paper I have been working entitled "Ambiguity and the language of long run risk".   The paper identifies and exploits a duality between the variational ambiguity model and the problem of long run asset valuation, which has been the subject of several important papers in finance and social discounting.  

The abstract is as follows:

This paper investigates a duality between ambiguity averse preferences and the valuation of long run risky assets or public projects.  The variational ambiguity model represents preferences over ambiguous acts via a minimization problem, and is fundamentally non-probabilistic.  In contrast, long run risky assets are ranked via a large maturity limit of expected discounted returns.  Despite their apparent differences, we show that each variational ambiguity preference is a long run risk preference, and (under natural conditions) vice versa.  We explore three implications: a notion of long run stochastic dominance that resolves differences between stochastic processes considered identical by standard risk measures, a typology of stochastic processes that pinpoints when a non-probabilistic description of long run risk is required, and an evolutionary foundation for variational ambiguity preferences that offers a novel explanation for ambiguity aversion.

I'd very much value any feedback you may have on these ideas; this is somewhat new territory for me so I am certain I can learn a lot from you all.

Best wishes for the new year,

Antony Millner