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Article Fröbenius Expansions for Second-Order Random Differential Equations: Stochastic Analysis and Applications to Lindley-Type Damping Models(Elsevier, 2026) Zeghdoudi, Halim; Kerker, Mohamed Amine; Boduroglu, ElifThis paper develops a Frobenius series framework for the stochastic analysis of second-order random differential equations of the form Y(t) + A(t)Y(t) = 0, where the damping coefficient A(t) is a positive stochastic process and the initial conditions are square-integrable random variables. Assuming mean-square analyticity of A(t) in a neighborhood of the initial time, we establish existence and uniqueness of the solution in L2(Omega) and derive exponentially convergent truncation error bounds for the associated Frobenius expansion. The resulting series representation enables the numerical approximation of the probability density function of Y(t) via Monte Carlo simulation. To improve computational efficiency, a control variates strategy is incorporated for variance reduction. A comprehensive numerical study is conducted for a broad family of positive, right-skewed damping distributions, including the Lindley, XLindley, New XLindley (NXLD), Gamma-Lindley, Inverse-Lindley, Truncated-Lindley, Log-Lindley, and a newly proposed Mixed Lindley-Uniform model. The simulations illustrate how different tail behaviors and boundedness properties of the damping coefficient influence the stochastic dynamics and the accuracy of density estimation. Finally, stylized applications to option pricing and Value-at-Risk estimation are presented to illustrate how the Frobenius-based framework and control variates methodology can be embedded within standard uncertainty quantification workflows. Overall, the proposed approach provides a flexible and computationally efficient tool for the analysis of randomly damped dynamical systems.Article Citation - WoS: 1Citation - Scopus: 1Shaken, Stirred and Indebted: Firm-Level Effects of Earthquakes(Elsevier Science inc, 2024) Arin, K. Peren; Arnau, Josep Marti; Boduroglu, Elif; Celik, Esref Ugur; Marti Arnau, JosepUsing firm-level data from Turkiye, we investigate the effects of earthquakes on firms' balance sheets. We find that earthquakes increase firms' liabilities but have a smaller effect on firms' assets, both in magnitude and significance. Using surveys sent to the finance and/or accounting managers of the largest 100 firms in Turkiye we identify common themes in their perceptions. Our findings reveal a consensus among respondents attributing the increased liabilities to exchange rate depreciation and lower business activity following a disaster. Conversely, higher availability of external credit is associated with a decrease in liabilities. Our analysis also indicates that finance managers with higher educational attainment may be underestimating the effects of earthquakes.
