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BEGIN:VEVENT
DTSTAMP:20250331T122235Z
DTSTART:20250402T140000Z
DTEND:20250402T150000Z
SUMMARY:HIMR-sponsored Probability Seminar: Lane Hughston - Valuation of 
 a financial claim contingent on the outcome of a quantum measurement
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}g1yr-m8mybc
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DESCRIPTION:Lane Hughston (School of Computing\, Goldsmiths University of
  London) will speak at the HIMR-sponsered Probability seminar.\n\nTitle:
  Valuation of a financial claim contingent on the outcome of a quantum m
 easurement7\n\nAbstract: In this interdisciplinary study at the interfac
 e of finance theory and quantum theory\, we consider a rational agent wh
 o at time 0 enters into a financial contract for which the payout is det
 ermined by a quantum measurement at some time T > 0. The state of the qu
 antum system is given in the Heisenberg representation by a known densit
 y 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 eigenv
 alues of X determine the amount paid if the corresponding outcome is obt
 ained in the measurement. We use Gleason's theorem to prove\, under reas
 onable axioms\, that there exists a pricing state q which is equivalent 
 to the physical state p such that the pricing function ? takes the linea
 r form ?(X) = P0T tr(qX) for any claim X\, where P0T is the one-period d
 iscount factor. By ‘equivalent’ we mean that p and q share the same null
  space: that is\, for any |?? ? H one has p|?? = 0 if and only if q|? ? 
 = 0. We introduce a class of optimization problems and solve for the opt
 imal contract payout structure for a claim based on a given measurement.
  Then we consider the implications of the Kochen–Specker theorem in this
  setting and we look at the problem of forming portfolios of such contra
 cts. This work illustrates how ideas from the theory of finance can be s
 uccessfully applied in a non-Kolmogorovian setting. Based on work with L
 . G. Sánchez-Betancourt (University of Oxford). The paper can be found a
 t J. Phys. A: Math. Theor. 57 (2024) 285302.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:G.205\, Alan Turing Building\, Manchester
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