de Vylder, F.; Goonvaerts, M. J.; Kaas, R. Stochastic processes defined from a Lagrangian. (English) Zbl 0756.60104 Insur. Math. Econ. 11, No. 1, 55-69 (1992). Summary: Let us consider a physical particle with movement described by a Lagrangian function. Then its classical deterministic trajectory \(x(t)\) \((t_ a\leq t\leq t_ b)\) between to fixed time-instants \(t_ a\) and \(t_ b\) can be replaced by a stochastic path \(X_ t\) \((t_ a\leq t\leq t_ b)\) such that \(x(t)=EX_ t\). Process \(X_ t\) defined in this way can be used to construct models for several actuarial situations. For instance, the rather deterministic analysis of underwriting cycles by G. C. Taylor [An analysis of underwriting cycles and their effects on insurance solvency. In: Managing the insolvency risk of insurance companies, ed. by J. D. Cummins and A. Derrig (Dordrecht, 1991)] can be probabilized. Movements, oscillatory on the average, with damping effects or not, with exterior perturbative forces or not, all time-dependent or not, can be introduced. We present the general theory with the two particular cases, one of which is the Brownian motion. Specific actuarial applications shall be treated in forthcoming publications. Cited in 3 Documents MSC: 60K99 Special processes 60J99 Markov processes Keywords:problem of solvency; Brownian motion; actuarial applications PDFBibTeX XMLCite \textit{F. de Vylder} et al., Insur. Math. Econ. 11, No. 1, 55--69 (1992; Zbl 0756.60104) Full Text: DOI References: [1] Feynman, R. P.; Hibbs, A. R., Quantum Mechanics and Path Integrals (1965), McGraw-Hill: McGraw-Hill New York · Zbl 0176.54902 [2] Goovaerts, M. J.; De Vylder, F.; Kaas, R., A stochastic approach to insurance cycles, Insurance: Mathematics and Economics, 11, 2 (1992), forthcoming · Zbl 0760.62095 [3] Grosjean, C. C.; Goovaerts, M. J., The analytical evaluation of one-dimensional Gaussian path-integral, Journal of Computational and Applied Mathematics, 311-331 (1988) · Zbl 0631.28004 [4] Taylor, G. C., An analysis of underwriting cycles and their effects on insurance solvency, (Cummins, J. D.; Derrig, A., Managing the Insolvency Risk of Insurance Companies (1991), Kluwer: Kluwer Dordrecht) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.