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DTSTAMP:20260926T031736Z
SUMMARY:Finance and Stochastics Seminar – Martin Herdegen
DESCRIPTION:Speaker: Martin Herdegen\nTitle: Optimal Investment and Consump
 tion in a Stochastic Factor Model\nAbstract: In this talk\, we study optim
 al investment and consumption in an incomplete stochastic factor model for
  a power utility investor on the infinite horizon.When the state space of 
 the stochastic factor is finite\, we give a complete characterisation of t
 he well-posedness of the problem\, and provide an efficient numerical algo
 rithm for computing the value function. When the state space is a (possibl
 y infinite) open interval and the stochastic factor is represented by an I
 tô diffusion\, we develop a general theory of sub- and supersolutions for
  second-order ordinary differential equations on open domains without boun
 dary values to prove existence of the solution to the Hamilton-Jacobi-Bell
 man (HJB) equation along with explicit bounds for the solution. By charac
 terising the asymptotic behaviour of the solution\, we are also able to pr
 ovide rigorous verification arguments for various models\, including — f
 or the first time — the Heston model. Finally\, we link the discrete an
 d continuous setting and show that the value function in the diffusion set
 ting can be approximated very efficiently through a fast discretisation sc
 heme. The talk is based on joint work with Florian Gutekunst and David Ho
 bson.
URL:https://www.imperial.ac.uk/events/213759/finance-and-stochastics-semina
 r-martin-herdegen/
DTSTART;TZID=Europe/London:20261006T140000
DTEND;TZID=Europe/London:20261006T150000
LOCATION:140\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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