Valuation of a Financial Claim Contingent on the Outcome of a Quantum Measurement
Hughston, L P and SánchezBetancourt, L. 2024. Valuation of a Financial Claim Contingent on the Outcome of a Quantum Measurement. Journal of Physics A: Mathematical and Theoretical, 57(28), 285302. ISSN 17518113 [Article]

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Abstract or Description
We consider a rational agent who at time 0 enters into a ﬁnancial contract for which the payout is determined by a quantum measurement at some time T > 0. The state of the quantum system is given in the Heisenberg representation by a known density matrix p. How much will the agent be willing to pay at time 0 to enter into such a contract? In the case of a ﬁnite dimensional Hilbert space H, each such claim is represented by an observable X where the eigenvalues of X determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state q which is equivalent to the physical state p such that the pricing function Π takes the linear form Π (X) = P_0T tr(q X) for any claim X, where P_0T is the oneperiod discount factor. By "equivalent" we mean that p and q share the same null space: thus, for any ξ〉∈ H one has pξ〉 = 0 if and only if qξ〉 = 0. We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the KochenSpecker theorem in this setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multiperiod contracts.
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Article 

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Data Access Statement: 
No new data were created or analysed in this study. 

Keywords: 
Quantum mechanics, quantum measurement, contingent claims, discount bonds, absence of arbitrage, rate of return, density matrices, Gleason’s theorem, KochenSpecker theorem 

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Item ID: 
36368 

Date Deposited: 
20 May 2024 15:12 

Last Modified: 
18 Jul 2024 10:49 

Peer Reviewed: 
Yes, this version has been peerreviewed. 

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