The aim of the paper is twofold. Firstly, to analyze the historical data of the earthquakes in the boarder area of Greece and then to produce a reliable model for the risk dynamics of the magnitude of the earthquakes, using advanced techniques from the Extreme Value Theory. Secondly, to discuss briefly the relevant theory of incomplete markets and price earthquake catastrophe bonds, combining the model found for the earthquake risk and an appropriate model for the interest rate dynamics in an incomplete market framework. The paper ends by providing some numerical results using Monte Carlo simulation techniques and stochastic iterative equations.

The aim of the paper is twofold. Firstly, to analyze the historical data of the earthquakes in the boarder area of Greece and then to produce a reliable model for the risk dynamics of the magnitude of the earthquakes, using advanced techniques from the Extreme Value Theory. Secondly, to discuss briefly the relevant theory of incomplete markets and price earthquake catastrophe bonds, combining the model found for the earthquake risk and an appropriate model for the interest rate dynamics in an incomplete market framework. The paper ends by providing some numerical results using Monte Carlo simulation techniques and stochastic iterative equations.

This paper investigates the problem of premium and reinsurance control of an ordinary insurance system when liabilities are driven by a fractional Brownian motion. The reserve equation is considered using two alternative routes: the first with no reinsurance option, and the second with some controllable proportional reinsurance coverage. Recent results from the theory of fractional linear-quadratic control (fractional calculus) are discussed, partially extended and utilized to derive compact analytical formulae for the optimal functionals of the safety loading (consequently for the respective premium rate), and the volume of the retained risk (or equivalently, for the proportion of the reinsurance coverage).

This article considers a defined-contribution pension scheme. It focuses in the post-retirement period and investigates the problem of controlling the level of payment of a variable annuity. The general version of the model is solved assuming a vector control variable differentiating the payments for each pensioner according to his age and an enhanced version for the market behavior, modeled via a multidimensional correlated fractional Brownian motion. Then, a reduced version of the basic model is also examined assuming an identical payment rate for all pensioners and a modified version of the typical Black-Scholes model driven by a standard fractional Brownian motion. Finally, a numerical application is developed for investigating the different investment strategies and also exploring the impact of the Hurst exponent in the final formula.