Making No-Arbitrage Discounting-Invariant: A New FTAP Version Beyond NFLVR and NUPBR
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Date
2022-06
Publication Type
Journal Article
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yes
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Abstract
What is absence of arbitrage for non-discounted prices? How can one define this so that it does not change meaning if one decides to discount after all?
The answer to both questions is a new discounting-invariant no-arbitrage concept. As in earlier work, we define absence of arbitrage as the zero strategy or some basic strategies being maximal. The key novelty is that maximality of a strategy is defined in terms of share holdings instead of value. This allows us to generalise both NFLVR, by dynamic share efficienc, and NUPBR, by dynamic share viability. These new concepts are the same for discounted or undiscounted prices, and they can be used in general models under minimal assumptions on asset prices. We establish corresponding versions of the FTAP, i.e., dual characterisations in terms of martingale properties. As one expects, "properly anticipated prices fluctuate randomly", but with an endogenous discounting process which cannot be chosen a priori. An example with N geometric Brownian motions illustrates our results.
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published
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Journal / series
Volume
1 (2)
Pages / Article No.
249 - 286
Publisher
American Institute of Mathematical Sciences
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Software
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Subject
Absence of arbitrage; maximal strategies; semimartingales; discounting; NFLVR; NUPBR; FTAP; σ; share maximal; dynamic share viability; Black-Scholes model
Organisational unit
03658 - Schweizer, Martin / Schweizer, Martin