We consider a nonstandard ruin problem where: (i) the increments of the process are heavy-tailed and Markov-dependent, modulated by a general Harris re- current Markov chain; (ii) ruin occurs when a positive boundary is attained within a sufficiently small time. Our main result provides sharp asymptotics for the small-time probability of ruin, viz., P(supn≤δu Sn ≥ u), where {Sn} denotes the discrete partial sums of the process and δ ∈ (0, 1/μ), where μ is the mean drift. We apply our results to obtain risk estimates which quantify, e.g., repetitive operational risk losses or the extremal behavior for a GARCH(1, 1) process.
['Jeffrey F. Collamore', 'Andrea Höing']
Small-time ruin for a financial process modulated by a Harris recurrent Markov chain