Abstract In this paper, we characterize two deterministic implied volatility models, defined by assuming that either the per-delta or the per-strike implied volatility surface has a deterministic evolution. Practitioners have recently proposed these two models to describe two regimes of implied volatility (see Derman (1999 Risk 4 55–9)). In an arbitrage-free sticky-delta model, we show that the...

We study parameter estimation for discretely observed stochastic differential equations driven by small Levy noises. There have been many applications of small noise asymptotics to mathematical finance and insurance. Using small noise models we can deal with both applications and statistical inference. We do not impose Lipschitz condition on the dispersion coefficient function and any moment co...

Based on the theory of independently scattered random measures, we introduce a natural generalisation Gaussian space-time white noise to Levy-type setting, which call Levy-valued measures. We determine subclass cylindrical Levy processes correspond and describe elements this uniquely by their characteristic function. embed measure, or corresponding process, in space general tempered distributio...

It is well known that for laminated composite plates a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of laminated composite plates with ar...

Conjugate pairs of distributions over infinite dimensional spaces are prominent in machine learning, particularly due to the widespread adoption of Bayesian nonparametric methodologies for a host of models and applications. Much of the existing literature in the learning community focuses on processes possessing some form of computationally tractable conjugacy as is the case for the beta proces...