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...

We identify possible long-run market shares and the long-run asset price dynamics of financial markets with heterogenous interacting agents. This involves stability conditions for a class of difference equation in a random environment, where the random environment is endogenously generated by...

The estimation of P(S-n u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n u) = nP(S, u, M-n = Y-n), where M-n = max(Y-1,...,...

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...

Stock returns exhibit heavy tails and volatility clustering. These features, motivating the use of GARCH models, make it difficult to predict times and sizes of losses that might occur. Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of...