Seminario interdisciplinare
ore
14:30
presso <i>aula non fissata</i>
Many optimization problems in theoretical and applied science are
difficult to solve: they exhibit multiple local optima or are not
’well-behaved’ in other ways (e.g., have discontinuities in the
objective function). The still-prevalent approach to handling such
difficulties -- other than ignoring them -- is to adjust or reformulate
the problem until it can be solved with standard numerical methods.
Unfortunately, this often involves simplifications of the original
problem; thus we obtain solutions to a model that may or may not reflect
our initial problem. But there is yet another approach: the application
of optimization heuristics like Simulated Annealing
or Genetic Algorithms. These methods have been shown to be capable of
handling non-convex optimization problems with all kinds of constraints,
and should thus be ideal candidates for many optimization problems. In
this talk we motivate the use of such methods by first presenting some
examples from finance for which optimization is required, and where
standard methods often fail. We briefly review some heuristics, and look
into their application to finance problems. We will also discuss the
stochastics of the solutions obtained from
heuristics, in particular we compare the randomness generated by the
optimization methods with the randomness inherent to the problem.