We prove functional central and non-central limit theorems for generalized variations of the anisotropic d-parameter fractional Brownian sheet (fBs) for any natural number d. Whether the central or the non-central limit theorem applies depends on the Hermite rank of the variation functional and...

Weather derivatives provide a tool for weather risk management, and the markets for these exotic financial products are gradually emerging in size and importance. This unique monograph presents a unified approach to the modeling and analysis of such weather derivatives, including financial...

This note deals with the asymptotic behavior of a weak solution of the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We study the solution given by the Feynman–Kac formula by the method of moments.

In the case where the parameters H1 and H2 belong to (1/2,1), Feyel and De La Pradelle (1991) have introduced a representation of the usual fractional Brownian sheet {Bs,tH1,H2}(s,t)∈R+2, as a stochastic integral over the compact rectangle [0,s]×[0,t], with respect to the Brownian sheet. In...

The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform...

Incomplete markets provide many challenges for both investment decisions and valuationproblems. While both problems have received extensive attention in complete markets,there remain many open areas in the theory of incomplete markets. We present the resultsin three parts. In the first essay we...

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the...