Finite-time ruin probabilities of bidimensional risk models with correlated Brownian motions

TL;DR

This paper derives new results for the probability of simultaneous ruin within finite time in two-dimensional risk models driven by correlated Brownian motions, advancing risk theory with dependence structures.

Contribution

It introduces novel methods to compute finite-time ruin probabilities in bidimensional models with correlated Brownian motions, expanding the theoretical framework of risk processes.

Findings

Derived explicit formulas for ruin probabilities

Analyzed the impact of correlation on ruin risks

Enhanced understanding of dependence in risk models

Abstract

The present work concerns the finite-time ruin probabilities for several bidimensional risk models with constant interest force and correlated Brownian motions.} Under the condition that the two Brownian motions $\{B_1(t), t\ge 0\}$ and $\{B_2(t), t\ge 0\}$ are correlated, we establish new results for the finite-time ruin probabilities. \textcolor{blue} {Our research has enriched the development of the ruin theory with heavy tails in unidimensional risk models and the dependence theory of stochastic processes.