We study the minimal/endogenous solution R to the maximum recursion on weighted branching trees given by R=D(⋁i=1NCiRi)∨Q, where (Q,N,C1,C2,…) is a random vector with N∈N∪{∞}, P(|Q|0)0 and nonnegative weights {Ci}, and {Ri}i∈N is a sequence of i.i.d. copies of R independent of...

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of...

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to...

Summary We propose an estimate for the index of extreme value distribution which based on k n -record values and show its consistency and asymptotic normality. The problem of specifying the optimal value of k  =  k n involved in our estimator is investigated. Some simulation results are also...

The Pareto model is very popular in risk management, since simple analytical formulas can be derived for financial downside risk measures (value-at-risk, expected shortfall) or reinsurance premiums and related quantities (large claim index, return period). Nevertheless, in practice,...