In theoretical ecology, simple stochastic models that satisfy two basic conditions about the distribution of niche values and feeding ranges have proved successful in reproducing the overall structural properties of real food webs, using species richness and connectance as the only input...

Mechanisms that enable declining networks to avert structural collapse and performance degradation are not well understood. This knowledge gap reflects a shortage of data on declining networks and an emphasis on models of network growth. Analyzing 700,000 transactions between firms in the New...

We introduce an innovative theoretical framework to model derivative transactions between defaultable entities based on the principle of arbitrage freedom. Our framework extends the traditional formulations based on Credit and Debit Valuation Adjustments (CVA and DVA). Depending on how the...

We suggest an empirical model of investment strategy returns which elucidates the importance of non-Gaussian features, such as time-varying volatility, asymmetry and fat tails, in explaining the level of expected returns. Estimating the model on the (former) Lehman Brothers Hedge Fund Index...

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the ?rst 5 terms of the expansions. A method to compute all the terms by induction is also given. At the money, we have a closed form formula for implied...

The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level...

The global financial system has become highly connected and complex. Has been proven in practice that existing models, measures and reports of financial risk fail to capture some important systemic dimensions. Only lately, advisory boards have been established in high level and regulations are...

The inverse first passage time problem asks whether, for a Brownian motion $B$ and a nonnegative random variable $\zeta$, there exists a time-varying barrier $b$ such that $\mathbb{P}\{B_sb(s),0\leq s\leq t\}=\mathbb{P}\{\zetat\}$. We study a "smoothed" version of this problem and ask whether...