2021/06/25 by Konrad Krystecki, Krystecki, Konrad
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2106.13533
openalex publication_date 2021/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (W1(s), W2(t)), s,t≥ 0 be a bivariate Brownian motion with standard Brownian motion marginals and constant correlation ρ∈ (-1,1). Parisian ruin is defined as a classical ruin that happens over an extended period of time, the so-called time-in-red. We derive exact asymptotics for the non-simultaneous Parisian ruin of the company conditioned on the event of non-simultaneous ruin happening. We are interested in finding asymptotics of such problem as u → ∞ and with the length of time-in-red being of order (1)/(u2), where u represents initial capital for the companies. Approximation of this problem is of interest for the analysis of Parisian ruin probability in bivariate Brownian risk model, which is a standard way of defining prolonged ruin models in the financial markets.