We solve the general problem of optimal risk sharing among a nite number of agents with limited liability. We show that the optimal allocation is characterized by endogenously determined ranks assigned to the participating agents and a hierarchical structure of risk sharing, where all agents...

This is the first part of a book I started writing in the year 2008 under the title of Sad Triology: The Crisis of a Nation. I name this chapter the Delirium as it represents the political response to what happens in the country due to the international outrage and pressures to Darfur Crisis....

Variable annuities have become popular retirement and investment vehicles due to their attractive guarantee features. Nonetheless, managing the financial risks associated with the guarantees poses great challenges for insurance companies. One challenge is risk quantification, which involves...

The recent analytical closed-form result ('http://ssrn.com/abstract=2549033' http://ssrn.com/abstract=2549033) discovered by Market Memory Trading L.L.C. (“MMT”) for the probability density function of the European style options with stochastic volatility, considered within the Heston model,...

The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...

The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk...

• The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications "Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options -- True...

•The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publication “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True...