BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Statistical Laboratory Graduate Seminars
SUMMARY:The Merton Problem with a drawdown constraint on c
onsumption - Arun Thillaisundaram (University of C
ambridge)
DTSTART;TZID=Europe/London:20120521T133000
DTEND;TZID=Europe/London:20120521T143000
UID:TALK38033AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/38033
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 1971\, many variants of the original problem h
ave been put forward and extensively studied. The
variant we consider here is the Merton problem wit
h a drawdown constraint on consumption. That is\,
the consumption can never fall below a fixed propo
rtion of the running maximum of past consumption.
In terms of economic motivation\, this constraint
represents a type of habit formation where once an
investor has reached a certain standard of living
\, he is reluctant to let his standard of living f
all too far below that level.\n\nTo be precise\, w
e consider an agent who can invest in a risk-free
asset and a risky stock modelled by geometric Brow
nian motion. The agent seeks to maximise the expec
ted infinite horizon utility of consumption by fin
ding the optimal portfolio selection and consumpti
on strategies – subject to the drawdown constraint
on consumption.\n\nWe consider power utility func
tions and use techniques from stochastic optimal c
ontrol to identify a candidate solution. Finally\,
we discuss how to verify our conjectured solution
.\n
LOCATION:CMS\, MR14
CONTACT:Elena Yudovina
END:VEVENT
END:VCALENDAR