HJB equation

Monday, June 11, 2018 - 11:00am - 11:30am
Tao Pang (North Carolina State University)
In the real world, the historical performance of a stock may have impacts on its dynamics and this suggests us to consider models with delays. We consider some portfolio optimization problem of Merton’s type in which the risky asset is described by some stochastic delay models. By virtue of the dynamic programming principle, we derive the Hamilton-Jacobi-Bellman (HJB) equations, which turn out to be nonlinear degenerate partial differential equations.
Tuesday, May 8, 2018 - 9:00am - 9:50am
Paul Dupuis (Brown University)
A number of methods have been developed for unbiased and efficient approximation of small probabilities and expected values that depend heavily on tail events. Examples include importance sampling and particle splitting methods. However, successfully implementing these methods can require some care. Traditional diagnostics one might use to assess algorithm performance can be misleading, and may suggest the method is working well when in fact it is not. As a consequence, methods that combine design with rigorous performance analysis are particularly useful.
Monday, May 7, 2018 - 2:00pm - 2:50pm
Shuenn-jyi Sheu (National Central University)
A review is given to the recent developments of the studies for the continuous time Merton portfolio optimization problems. They include risk-sensitive portfolio optimization problems, upside chance and downside risk probabilities optimization and optimal consumption problems. The developments follow by the ideas of Fleming(1995) given in IMA Vol, which suggests to reformulate the risk-sensitive optimization problem as a risk-sensitive stochastic control problem.
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