Abhinav Anand

Abhinav Anand

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Duality and Asset Pricing

6 minute read

Published:

The duality framework from Reflections on Duality maps onto asset pricing with very little friction. The payoff space is the primal space, the stochastic discount factor is the dual element, and the pricing formula is the bilinear pairing. Most of the central results in theoretical asset pricing — the Hansen-Jagannathan bound, the existence of risk-neutral measures, the non-uniqueness of the SDF in incomplete markets — are direct consequences of the Hilbert space machinery once the identification is made.

Reflections on Duality

4 minute read

Published:

Every duality result answers one question: given a space of states, what are all the ways to assign weights to those states and collapse them into a single number? The dual space \(V^*\) is the totality of such weighting schemes. The bilinear pairing \(\langle \varphi, x \rangle = \varphi(x)\) is the aggregation step.