In this paper, we propose a Fenchel duality approach to study the minimization problem of the shortfall risk. We consider a general increasing and strictly convex loss function, which may be more general than the situation of convex risk measures usually assumed in the literature. We first...

In this paper, we propose a general data-driven framework that unifies the valuation and risk measurement of financial derivatives, which is especially useful in markets with thinly-traded derivatives. We first extract the empirical characteristic function from market-observable time series for...

In this paper, we propose a general data-driven framework that unifies the valuation and risk measurement of financial derivatives, which is especially useful in markets with thinly-traded derivatives. We first extract the empirical characteristic function from market-observable time series for...

In this paper, we propose an efficient approach to the calculation of risk measures for an insurer's liability from writing a variable annuity with guaranteed benefits. Our approach is based on a novel application of the Hermite series expansions on the transition density of a diffusion process...