We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressions for the asymptotic covariance matrix. We develop in detail the martingale estimating function ap...

We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and lower bounds, in terms of bounds on the correlation, for the value V B of the exponential utility ma...

This paper mainly deals with the almost surely exponential stability and exponential p-th moment stability for a class of stochastic Cohen–Grossberg neural networks with distributed delays and reaction–diffusion term. By constructing suitable Lyapunov functional, employing the nonnegative semi-martingale convergence theorem and applying matrix theory and stochastic analysis technique, two delay...

1.1. Review. Let F := {Ft}t≥0 be a filtration of the probability space (Ω,F ,P) and let Mt = M(t) be a martingale relative to F. Assume that M(t) has continuous sample paths. For any stopping time τ denote by Fτ the stopping field associated with τ, that is, (1) Fτ := {A ∈ F : A ∩ {τ ≤ t} ∈ Ft ∀ t ≥ 0}. Proposition 1. (Doob’s Maximal Inequality) If Mt is a continuous martingale such that E|MT| ...

We prove a robust super-hedging duality result for path-dependent options on assets with jumps in continuous-time setting. It requires that the collection of martingale measures is rich enough and payoff function satisfies some continuity property. by-product quasi-sure version optional decomposition theorem, which can also be viewed as functional Itô’s lemma applies to non-smooth functionals (...

We shed light on the characteristics of high-frequency asset return and volatility processes and their implications for daily return distributions. We document that the standard jumpdiffusion setting readily accommodates the main features of equity index returns, including stochastic volatility, outlier behavior and a strong asymmetry between return and volatility innovations. We also informall...

In this article the problem of the American option valuation in a Lévy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying proces...