We use a discrete time analysis, giver necessary and sufficient conditions for the almost sure convergence of ARCH(1) and GARCH(1,1) discrete time models, to suggest an extension of the (G)ARCH concept to continuous time processes. The models, based on a single background driving Lévy process,...

There has been an on-going debate about choices of the most suitable model amongst avariety of model specifications and parameterizations. The first dissertation essay investigateswhether asymmetric leptokurtic return distributions such as Hansen’s (1994) skewed tdistributioncombined with...

There has been an on-going debate about choices of the most suitable model amongst a variety of model specifications and parameterizations. The first dissertation essay investigates whether asymmetric leptokurtic return distributions such as Hansen's (1994) skewed tdistribution combined with...

For a continuous-time financial market with a single agent, we establish equilibrium pricing formulae under the assumption that the dividends follow an exponential Lévy process. The agent is allowed to consume a lump at the terminal date; before, only flow consumption is allowed. The agent's...

This article shows that the nonstandard approach to stochastic integration with respect to (C^2 functions of) Lévy processes is consistent with the classical theory of pathwise stochastic integration with respect to (C^2 functions of) jump-diffusions with finite-variation jump part.It is proven...

The main aim of this thesis is the development of locally risk-minimizing hedging strategies for unit-linked life insurance contracts whose unit is modeled in a general Lévy-process financial market. It therefore merges the quite advanced and in recent years developed theory of...

We investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes...

In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration {F t } tÏ0 {Ft}tÏ0 is generated by an information process {ξ t } tÏ0 {ξt}tÏ0 defined in such a way that at some fixed time T an F T FT -measurable random variable X T XT is "revealed". A cash...

In this paper, we present a stochastic optimal control model to optimize an insurance firm problem in the case where its cash-balance process is assumed to be described by a stochastic differential equation driven by Teugels martingales. Noticing that the insurance firm is able to control its...