The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This...

We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of...

Abstract In this paper we introduce the well-balanced Lévy driven Ornstein–Uhlenbeck process as a moving average process of the form X t  = ∫ exp(- λ | t - u |) dL u . In contrast to Lévy driven Ornstein–Uhlenbeck processes the well-balanced form possesses continuous sample paths and...

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...

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...

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...

With the acceptance of the new Basel II banking regulation (implemented in South Africa in January 2008) the search for improved ways of modeling the most important banking activities has become very topical. Since the notion of Levy-process was introduced, it has emerged as an important tool...

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are...