XII Symposium of Probability and Stochastic Processes

Part of the Progress in Probability Book Series (volume 73)

Editors: Hernández-Hernández, Daniel; Pardo, Juan Carlos; Rivero, Victor

DOI: 10.1007/978-3-319-77643-9

ISBN: 978-3-319-77642-2

Publisher: Springer International Publishing - Springer Journals

Jun 27, 2018

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Scaling Limits of Markov-Branching Trees and Applications

Haas, Bénédicte

Pages: 3 –50

[The goal of these lecture notes is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.]
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Optimality of Two-Parameter Strategies in Stochastic Control

Yamazaki, Kazutoshi

Pages: 51 –104

[In this note, we study a class of stochastic control problems where the optimal strategies are described by two parameters. These include a subset of singular control, impulse control, and two-player stochastic games. The parameters are first chosen by the two continuous/smooth fit conditions,...
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Asymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes

Kolkovska, Ekaterina T.; Martín-González, Ehyter M.

Pages: 107 –134

[We investigate a classical two-sided jumps risk process perturbed by a spectrally negative α-stable process, in which the gain size distribution has a rational Laplace transform. We consider three classes of light- and heavy-tailed claim size distributions. We obtain the asymptotic behaviors of...
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Characterization of the Minimal Penalty of a Convex Risk Measure with Applications to Robust Utility Maximization for Lévy Models

Hernández-Hernández, Daniel; Pérez-Hernández, Leonel

Pages: 135 –168

[The minimality of the penalty function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and closed subset of the absolutely continuous measures with...
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Blackwell-Nash Equilibria in Zero-Sum Stochastic Differential Games

Escobedo-Trujillo, Beatris Adriana; Jasso-Fuentes, Héctor; López-Barrientos, José Daniel

Pages: 169 –193

[Advanced-type equilibria for a general class of zero-sum stochastic differential games have been studied in part by Escobedo-Trujillo et al. (J Optim Theory Appl 153:662–687, 2012), in which a comprehensive study of the so-named bias and overtaking equilibria was provided. On the other hand, a...
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A Note on Γ-Convergence of Monotone Functionals

Aguilar, Erick Treviño

Pages: 195 –206

[In this note we present a criterion under which a functional defined on vectors of non-decreasing functions is the Γ-limit of a functional defined on vectors of continuous non-decreasing functions. To this end, we present a separation principle in which a weakly converging sequence of continuous...
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A Criterion for Blow Up in Finite Time of a System of 1-Dimensional Reaction-Diffusion Equations

Guerrero, Eugenio; López-Mimbela, José Alfredo

Pages: 207 –217

[We give a criterion for blow up in finite time of the system of semilinear partial differential equations ∂ui(t,x)∂t=12∂2uit,x∂x2+φi′xφix∂uit,x∂x+uj1+βit,x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
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A Note on the Small-Time Behaviour of the Largest Block Size of Beta n-Coalescents

Siri-Jégousse, Arno; Yuan, Linglong

Pages: 219 –234

[We study the largest block size of Beta n-coalescents at small times as n tends to infinity, using the paintbox construction of Beta-coalescents and the link between continuous-state branching processes and Beta-coalescents established in Birkner et al. (Electron J Probab 10(9):303–325, 2005)...

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XII Symposium of Probability and Stochastic Processes

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XII Symposium of Probability and Stochastic Processes

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