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UID:ff674cb0a64711481af5669e0db30218
DTSTAMP:20240412T181433Z
SUMMARY:Martin Herdegen: Bubbles in Discrete Time Models
DESCRIPTION:We introduce a new definition of bubbles in discrete-time model
s based on the discounted stock price losing mass at some finite drawdown
under an equivalent martingale measure. We provide equivalent probabilisti
c characterisations of this definition and give examples of discrete-time
martingales that are bubbles and those that are not. In the Markovian case
\, we provide sufficient analytic conditions for the presence of bubbles.
We also show that the existence of bubbles is directly linked to the exist
ence of a non-trivial solution to a linear Volterra integral equation of t
he second kind involving the Markov kernel. Finally\, we show that our def
inition of bubbles in discrete time is consistent with the strict local ma
rtingale definition of bubbles in continuous time in the sense that a prop
erly discretised strict local martingale in continuous time is a bubble in
discrete time. The talk is based on joint work with DÃ¶rte Kreher.
URL:https://www.imperial.ac.uk/events/149413/martin-herdegen-bubbles-in-dis
crete-time-models/
DTSTART;TZID=Europe/London:20220622T133000
DTEND;TZID=Europe/London:20220622T143000
LOCATION:Room 140\, Huxley Building\, South Kensington Campus\, Imperial Co
llege London\, London\, SW7 2AZ\, United Kingdom
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