Orateur
Description
This talk will focus on a new type of quantile optimization problems arising
from insurance contract design models. This type of optimization problems is
characterized by a constraint that the derivatives of the decision quantile
functions are bounded. Such a constraint essentially comes from the
“incentive compatibility” constraint for any optimal insurance contract to
avoid the potential severe problem of moral hazard in insurance contract
design models. By a further development of the relaxation method, we
provide a systemic approach to solving this new type of quantile optimization
problems. The optimal quantile is expressed via the solution of a free
boundary problem for a second-order nonlinear ordinary differential equation
(ODE), which is similar to the Black-Scholes ODE for perpetual American
options.
