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SUMMARY:The Merton Problem for Optimal Investment - Arun Thillaisundaram (
 University of Cambridge)
DTSTART:20111117T150000Z
DTEND:20111117T160000Z
UID:TALK33787@talks.cam.ac.uk
CONTACT:Elena Yudovina
DESCRIPTION:The Merton problem – a question about optimal portfolio sele
 ction and consumption in continuous time – is indeed ubiquitous througho
 ut the mathematical finance literature. Since Merton’s seminal paper in 
 1969\, many variants of the original problem have been put forward and ext
 ensively studied. First we will consider the standard Merton problem. To b
 e 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 consumption by finding the 
 optimal portfolio selection and consumption strategies. We work with power
  utility functions because they enable us to construct explicit solutions.
  If time permits\, we will also consider a variant of the original problem
  where we impose a drawdown constraint on consumption. That is\, the consu
 mption can never fall below a fixed proportion of the running maximum of p
 ast consumption. 
LOCATION:CMS\, MR9
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