Modeling, Analysis, and Optimization for Mathematical Finance, Economics, and Risks is a critical domain that integrates mathematical theory with practical applications to address the complexities of modern financial and economic systems. This special issue focuses on recent studies that are...

The paper builds a Variance-Gamma (VG) model with five parameters: location (μ), symmetry (δ), volatility (σ), shape (»), and scale (θ); and studies its application to the pricing of European options. The results of our analysis show that the five-parameter VG model is a stochastic...

It is shown that moments of negative order as well as positive non- integral order of a nonnegative random variable X can be expressed by the Laplace transform of X. Applying these results of certain first passage times gives explicit formulae for moments of suprema of Bessel processes as well...

In this paper we introduce a fractionally integrated exponential continuous time GARCH(p,d,q) process. It is defined in such a way it is a continuous time extension of the discrete time FIEGARCH(p,d,q) process. We investigate stationarity and moment properties of the new model. It is also shown...

A Lévy process is observed at time points of distance delta until time T. We construct an estimator of the Lévy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and delta. Thereby, we encompass the usual low- and high-frequency assumptions...

In this paper we introduce an exponential continuous time GARCH(p, q) process. It is defined in such a way that it is a continuous time extension of the discrete time EGARCH(p, q) process. We investigate stationarity and moment properties of the new model. An instantaneous leverage effect can be...

Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels. We investigate classical and nonclassical stochastic volatility models with respect to their...

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process— a continuous-time process with stationary and independent increments— crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from...

We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are ergodic, the resulting estimators are consistent. We investigate the quality of our estimators in a...