Spring 2021 Simulation of an integro-differential equation and application in estimation of ruin probability with mixed fractional Brownian motion
Chunhao Cai, Weilin Xiao
J. Integral Equations Applications 33(1): 1-17 (Spring 2021). DOI: 10.1216/jie.2021.33.1

Abstract

We consider the numerical solution of one type of integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical Lévy process, but by the mixed fractional Brownian motion.

Citation

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Chunhao Cai. Weilin Xiao. "Simulation of an integro-differential equation and application in estimation of ruin probability with mixed fractional Brownian motion." J. Integral Equations Applications 33 (1) 1 - 17, Spring 2021. https://doi.org/10.1216/jie.2021.33.1

Information

Received: 30 October 2019; Accepted: 6 May 2020; Published: Spring 2021
First available in Project Euclid: 11 June 2021

Digital Object Identifier: 10.1216/jie.2021.33.1

Subjects:
Primary: 35R09 , 60G15 , 60G22

Keywords: estimation of ruin probability , fundamental martingale , Girsanov theorem , Integro-differential equation , mixed fractional Brownian motion

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

Vol.33 • No. 1 • Spring 2021
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