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SUMMARY:The Merton Problem with a drawdown constraint on consumption - Aru
 n Thillaisundaram (University of Cambridge)
DTSTART:20120521T123000Z
DTEND:20120521T133000Z
UID:TALK38033@talks.cam.ac.uk
CONTACT:Elena Yudovina
DESCRIPTION:The Merton problem - a question about optimal portfolio select
 ion and consumption in continuous time - is indeed ubiquitous throughout t
 he mathematical finance literature. Since Merton’s seminal paper in 1971
 \, many variants of the original problem have been put forward and extensi
 vely studied. The variant we consider here is the Merton problem with a dr
 awdown constraint on consumption. That is\, the consumption can never fall
  below a fixed proportion of the running maximum of past consumption. In t
 erms of economic motivation\, this constraint represents a type of habit f
 ormation where once an investor has reached a certain standard of living\,
  he is reluctant to let his standard of living fall too far below that lev
 el.\n\nTo 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 s
 eeks to maximise the expected infinite horizon utility of consumption by f
 inding the optimal portfolio selection and consumption strategies – subj
 ect to the drawdown constraint on consumption.\n\nWe consider power utilit
 y functions and use techniques from stochastic optimal control to identify
  a candidate solution. Finally\, we discuss how to verify our conjectured 
 solution.\n
LOCATION:CMS\, MR14
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