An accurate analytical approximation for the price of a European-style arithmetic Asian option.

For discrete arithmetic Asian options the payoff depends on the price average of the underlying asset. Due to the dependence structure between the prices of the underlying asset, no simple exact pricing formula exists, not even in a Black-Scholes setting. In the recent literature, several approximations and bounds for the price of this type of option are proposed. One of these approximations consists of replacing the distribution of the stochastic price average by an ad hoc distribution (e.g. Lognormal or Inverse Gaussian) with the same first and second moment. In this paper we use a different approach and combine a lower and upper bound into a new analytical approximation. This approximation can be calculated efficiently, turns out to be very accurate and moreover, it has the correct first and second moment. Since the approximation is analytical, we can also calculate the corresponding hedging Greeks and construct a replicating strategy.Options; Dependence; Structure; Prices; Hedging; Strategy;

The concept of comonotonicity in actuarial science and finance : theory.

n an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.Risk; Actuarial; Science; Theory;

Bounds for present value functions with stochastic interest rates and stochastic volatility.

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution.In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds.Distribution; Value; Cash flow; Interest rates; Researchers; Problems;

Stochastic macromodeling for hierarchical uncertainty quantification of nonlinear electronic systems

A hierarchical stochastic macromodeling approach is proposed for the efficient variability analysis of complex nonlinear electronic systems. A combination of the Transfer Function Trajectory and Polynomial Chaos methods is used to generate stochastic macromodels. In order to reduce the computational complexity of the model generation when the number of stochastic variables increases, a hierarchical system decomposition is used. Pertinent numerical results validate the proposed methodology

Combining Krylov subspace methods and identification-based methods for model order reduction

Many different techniques to reduce the dimensions of a model have been proposed in the near past. Krylov subspace methods are relatively cheap, but generate non-optimal models. In this paper a combination of Krylov subspace methods and orthonormal vector fitting (OVF) is proposed. In that way a compact model for a large model can be generated. In the first step, a Krylov subspace method reduces the large model to a model of medium size, then a compact model is derived with OVF as a second step