Advances in Applied Probability

We formulate a centrally planned portfolio selection problem with the investor and the manager having S-shaped utilities under a recently popular first-loss contract. We solve for the closed-form optimal portfolio, which shows that a first-loss contrac…

We consider Gaussian approximation in a variant of the classical Johnson–Mehl birth–growth model with random growth speed. Seeds appear randomly in at random times and start growing instantaneously in all directions with a random speed. The locations,…

We study the asymptotic growth rate of the labels of high-degree vertices in weighted recursive graphs (WRGs) when the weights are independent, identically distributed, almost surely bounded random variables, and as a result confirm a conjecture by Lod…

We consider linear preferential attachment trees with additive fitness, where fitness is the random initial vertex attractiveness. We show that when the fitnesses are independent and identically distributed and have positive bounded support, the local …

We study heterogeneously interacting diffusive particle systems with mean-field-type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates o…

Graphical models with heavy-tailed factors can be used to model extremal dependence or causality between extreme events. In a Bayesian network, variables are recursively defined in terms of their parents according to a directed acyclic graph (DAG). We …