There is good empirical evidence to show that the financial series, whether stocks or indices, currencies or interest rates do not follow the log-normal random walk underlying the Black-Scholes model, which is the basis for most of the theory of options valuation. This article presents a...

In this paper we consider properties and power expressions of the functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$f:(-1,1)\rightarrow \mathbb{R }$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$f_L:(-1,1)\rightarrow \mathbb{R }$$</EquationSource> </InlineEquation>, defined by <Equation ID="Equa1"> <EquationSource Format="TEX">$$\begin{aligned} f(x;\gamma )=\frac{1}{\pi }\int \limits _{-1}^1 \frac{(1+xt)^\gamma }{\sqrt{1-t^2}}\,\mathrm{d}t \quad...</equationsource></equation></equationsource></inlineequation></equationsource></inlineequation>

In this paper, we consider a perturbed compound Poisson risk model with investment and debit interests. Dividends are paid to the shareholders according to a threshold dividend strategy. An alternative assumption is that when the surplus is negative, a debit interest is applied and when the...

Following up on the work of Nadarajah and Teimouri [Nadarajah, S., Teimouri, M., 2012. On the characteristic function for asymmetric exponential power distributions. Econometric Reviews 31, 475–481], we derive here, for the first time, explicit closed-form expressions for the characteristic...