Financial Models with Defaultable Num\'eraires

TL;DR

This paper explores financial models where assets can devalue relative to each other, establishing conditions for local valuation rules to be combined into global arbitrage-free valuations.

Contribution

It introduces a framework for aggregating local valuation rules in models with potentially devaluing assets, ensuring arbitrage-free global valuations.

Findings

Conditions for local valuation rules to be combined globally

Framework for arbitrage-free valuation with devaluing assets

Method to handle multiple numeraires in financial models

Abstract

Financial models are studied where each asset may potentially lose value relative to any other. Conditioning on non-devaluation, each asset can serve as proper num\'eraire and classical valuation rules can be formulated. It is shown when and how these local valuation rules can be aggregated to obtain global arbitrage-free valuation formulas.