Modelling of tradeable securities with dividends

We propose a generalized framework for the modeling of tradeable securities with dividends which are not necessarily cash dividends at fixed times or continuously paid dividends. In our setup the dividend processes are only required to be semi-martingales. We give a definition of self-financing replication which incorporates dividend processes, and we show how this allows us to translate standard results for the pricing and hedging of derivatives on assets without dividends to the case of assets with dividends. We then apply this framework to analyze and compare the different assumptions that have been made in earlier dividend models. We also study the case where we have uncertain dividend dates, and we look at securities which are not equity-based such as futures and credit default swaps, since our weaker assumptions on the dividend process allow us to consider these other applications as well

Geography, culture, and religion: Explaining the bias in Eurovision song contest voting

This paper analyses votes cast in the Eurovision Song Contest in the period 1975 - 2003. We test whether accusations of 'political' voting among participants can be substantiated by looking at geographical influences. Our approach differs in two ways from earlier studies. First, we take into account a variety of variables to distinguish political voting from preferences based on cultural, linguistic, ethnic, and religious differences and similarities between countries. Secondly, we analyse the determinants of the voting behaviour separately per country, instead of looking at average effects over all participating countries. We find that geographical factors substantially affect the votes. Even after correction for cultural, linguistic and other factors many countries prefer or dislike the songs of surrounding countries. This leads to the suspicion that the geograph¬ical preferences reflect political voting. Also, we show that several countries favour songs of participants with the same religious background, while others prefer the contributions of countries with a different religion. Moreover, using data on the amount of Turkish immigrants across European countries, we document that countries with a substantial Turkish population favour the Turkish songs ('patriotic' voting). Furthermore, we study the repercussions of opening up the voting system to the general public by the introduction of televoting. It turns out that religious and patriotic voting have become considerably stronger since the introduction of the new voting system. Finally, we confront our em¬pirical findings to the publicly debated accusations of political voting made against certain blocks of countries. Although our analysis uncovers significant geographical patterns (suggesting political voting), we do hardly establish any empirical evidence for the claims against these particular countries

Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time $t_d$ during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of $t_d$, and tends to $0$ as time tends to $t_d^-$ with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of $t_d$. When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.

Approximation solutions for indifference pricing under general utility functions

With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners use: Best Estimate plus a "Market Value Margin". Furthermore, we compare our approximations to known analytical results for exponential and power utility

Optimal Concentration of Light in Turbid Materials

In turbid materials it is impossible to concentrate light into a focus with conventional optics. Recently it has been shown that the intensity on a dyed probe inside a turbid material can be enhanced by spatially shaping the wave front of light before it enters a turbid medium. Here we show that this enhancement is due to concentration of light energy to a spot much smaller than a wavelength. We focus light on a dyed probe sphere that is hidden under an opaque layer. The light is optimally concentrated to a focus which does not exceed the smallest focal area physically possible by more than 68%. A comparison between the intensity enhancements of both the emission and excitation light supports the conclusion of optimal light concentration.Comment: We corrected an ambiguous description of the focus size in our abstract and text pointed out by an anonymous refere

Digital optical phase conjugation of fluorescence in turbid tissue

We demonstrate a method for phase conjugating fluorescence. Our method, called reference free digital optical phase conjugation, can conjugate extremely weak, incoherent optical signals. It was used to phase conjugate fluorescent light originating from a bead covered with 0.5 mm of light-scattering tissue. The phase conjugated beam refocuses onto the bead and causes a local increase of over two orders of magnitude in the light intensity. Potential applications are in imaging, optical trapping, and targeted photochemical activation inside turbid tissue

Focusing through random media: eigenchannel participation number and intensity correlation

Using random matrix calculations, we show that, the contrast between maximally focused intensity through random media and the background of the transmitted speckle pattern for diffusive waves is, \mu_N =1 +N_{eff}, where N eff is the eigenchannel participation number for the transmission matrix. For diffusive waves, N_{eff} is the inverse of the degree of intensity correlation, \kappa. The profile of the focused beam relative to the ensemble average intensity is expressed in terms of the square of the normalized spatial field correlation function, F(\Delta r), and \kappa. These results are demonstrated in microwaves experiments and provide the parameters for optimal focusing and the limits of imaging

Optical phase conjugation with less than a photon per degree of freedom

We demonstrate experimentally that optical phase conjugation can be used to focus light through strongly scattering media even when far less than a photon per optical degree of freedom is detected. We found that the best achievable intensity contrast is equal to the total number of detected photons, as long as the resolution of the system is high enough. Our results demonstrate that phase conjugation can be used even when the photon budget is extremely low, such as in high-speed focusing through dynamic media, or imaging deep inside tissue