We investigate formation of economic and social networks where agents may form or cut ties. The novelty is combining a setup where agents are heterogeneous in their talent for generating value in the links they form and value may also accrue from indirect ties. We provide sufficient conditions...

Modern financial networks exhibit a high degree of interconnectedness and determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse. In the American Economic Review, Elliott, Golub and Jackson proposed a simple...

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models...

Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated behaviours find their origin in the theory of complex...

This note explores the mathematical theory to solve modern gamblers ruin problems. We establish a ruin framework and solve for the probability of bankruptcy. We also show how this relates to the expected time to bankruptcy and review the risk neutral probabilities associated an adjustment to...

We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We...

The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process $(X,D)$ of a diffusion state variable $X$ driving default intensity and a default indicator process...

We employ a wavelet approach and conduct a time-frequency analysis of dynamic correlations between pairs of key traded assets (gold, oil, and stocks) covering the period from 1987 to 2012. The analysis is performed on both intra-day and daily data. We show that heterogeneity in correlations...

Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation...

In this paper, we analyse the South African implied volatility in various setting. We assess the information content in SAVI implied volatility using daily markets data. Our empirical application is focused on the FTSE/JSE Top 40 index and we emphasize our models performance in distinct...