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CATEGORIES:Statistical Laboratory Graduate Seminars
SUMMARY:The Merton Problem for Optimal Investment - Arun T
hillaisundaram (University of Cambridge)
DTSTART;TZID=Europe/London:20111117T150000
DTEND;TZID=Europe/London:20111117T160000
UID:TALK33787AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/33787
DESCRIPTION:The Merton problem – a question about optimal port
folio selection and consumption in continuous time
– is indeed ubiquitous throughout the mathematica
l finance literature. Since Merton’s seminal paper
in 1969\, many variants of the original problem h
ave been put forward and extensively studied. Firs
t we will consider the standard Merton problem. To
be precise\, we consider an agent who can invest
in a risk-free asset and a risky stock modelled by
geometric Brownian motion. The agent seeks to max
imise the expected infinite horizon utility of con
sumption by finding the optimal portfolio selectio
n and consumption strategies. We work with power u
tility functions because they enable us to constru
ct explicit solutions. If time permits\, we will a
lso consider a variant of the original problem whe
re we impose a drawdown constraint on consumption.
That is\, the consumption can never fall below a
fixed proportion of the running maximum of past co
nsumption.
LOCATION:CMS\, MR9
CONTACT:Elena Yudovina
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