A random variable dominates another random variable with respectto the covariance order if the covariance of any two monotone increasingfunctions of this variable is smaller. We characterize completely thecovariance order, give strong sufficient conditions for it, present a numberof examples in...

We consider economic obstacles that limit the reliability and accuracy of value-at-risk (VaR). Investors who manage large market transactions should take into account the impact of the randomness of large trade volumes on predictions of price probability and VaR assessments. We introduce...

We consider the randomness of market trade as the origin of price and return stochasticity. We look at time series of trade values and volumes as random variables during the averaging interval Δ and describe the dependences of market-based volatilities of price and return on the volatilities...

Real Options analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to...

This paper presents probability distributions for price and returns random processes for averaging time interval Δ. These probabilities determine properties of price and returns volatility. We define statistical moments for price and returns random processes as functions of the costs and the...

Amid the controversies around the optimisation criteria and the objective functions when applying mathematical methods in economics, we proposed a method of quantifying a multi-criteria optimum, called critical distance method. The demonstration of this method is exemplified by assessing the...

The aim of this paper is to develop a hedging methodology for making a portfolio of options delta, vega and gamma neutral by taking positions in other available options, and simultaneously minimizing the net premium to be paid for the hedging. A quadratic programming solution for the problem is...

This paper proposes a methodology for active hedging Greeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid...

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we...

This paper is a supplement to Ghossoub [11]. In this supplement, some of the results of Ghossoub [11], as well as the techniques used to obtain these result are extended to a more general problem of demand for contingent claims with belief heterogeneity. Moreover, a general problem of monotone...