On Future Drawdowns of Lévy processes

2014/09/12 by Erik J. Baurdoux, Baurdoux, E. J., Zbigniew Palmowski +3
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1409.3780

openalex publication_date 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given Lévy process X=(X_t)_t∈ℝ+ and for fixed s∈ ℝ₊∪\∞\ and t∈ℝ₊ we analyse the \it future drawdown extremes that are defined as follows: D^*_t,s = sup_{0≤ u≤ t} inf_{u≤ w lt; t+s}(X_w-X_u), \underline D^*_t,s = inf_{0≤ u≤ t} inf_{u≤ w lt; t+s}(X_w-X_u). The path-functionals D^*_t,s and \underline D^*_t,s are of interest in various areas of application, including financial mathematics and queueing theory. In the case that X has a strictly positive mean, we find the exact asymptotic decay as x→∞ of the tail probabilities ℙ( D^*_t

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