We study the effect of the red card in a soccer game. A red card is given by a referee to signify that a player has been sent off following serious misconduct. The player who has been sent off must leave the game immediately and cannot be replaced during the game. His team must continue the game...

In this paper we studyy arithmetic Asian options when the underlying stock is driven by special semimartingale processes. We show that the inherently path dependent problem of pricing Asian options can be transformed into a problem without path dependence in the payoff function. We also show...

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.

We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability...

The main idea of this paper is to introduce Tradeable Measures of Risk as an objective and model independent way of measuring risk. The present methods of risk measurement, such as the standard Value-at-Risk supported by BASEL II, are based on subjective assumptions of future returns. Therefore...

In this paper we introduce a quantitative measure of the excitement of sports games. This measure can be thought of as the variability of the expectancy of winning as a game progresses. We illustrate the concept of excitement at soccer games for which the theoretical win expectancy can be well...

In this article, we define new 'Greeks' for financial derivatives: sensitivities to the running maximum and the running maximum drawdown of an underlying asset. Some types of portfolios, such as the net asset value of a hedge fund or performance fees, are sensitive to these parameters. In order...

This paper studies drawdown and drawup processes in a general diffusion model. The main result is a formula for the joint distribution of the running minimum and the running maximum of the process stopped at the time of the first drop of size a. As a consequence, we obtain the probabilities that...

In this article we study options on a traded account. In terms of the actions available to the buyer, the options we study are more general than a class of options known as {\em passport options}; in terms of the model of the underlying asset they are more restrictive. Using probabilistic...