On the Tail Probabilities of Aggregated Lognormal Random Fields with Small Noise

References

• Ahsan SM (1978) Portfolio selection in a lognormal securities market. Zeitschrift für Nationalokonomie—J. Econom. 38(1–2):105–118.Crossref, Google Scholar
• Asmussen S, Rojas-Nandayapa L (2008) Asymptotics of sums of lognormal random variables with Gaussian copula. Statist. Probab. Lett. 78(16):2709–2714.Crossref, Google Scholar
• Basak S, Shapiro A (2001) Value-at-risk-based risk management: Optimal policies and asset prices. Rev. Financial Stud. 14(2):371–405.Crossref, Google Scholar
• Borell C (1975) The Brunn-Minkowski inequality in Gaussian space. Inventiones Mathematicae 30(2):207–216.Crossref, Google Scholar
• Deutsch HP (2004) Derivatives and Internal Models, 3rd ed. (Palgrave Macmillan, Basingstoke, UK).Google Scholar
• Duffie D, Pan J (1997) An overview of value at risk. J. Derivatives 4(3):7–49.Crossref, Google Scholar
• Dufresne D (2001) The integral of geometric Brownian motion. Advances Appl. Probab. 33(1):223–241.Crossref, Google Scholar
• Foss S, Richards A (2010) On sums of conditionally independent subexponential random variables. Math. Oper. Res. 35(1):102–119.Link, Google Scholar
• Gao X, Xu H, Ye D (2009) Asymptotic behavior of tail density for sum of correlated lognormal variables. Internat. J. Math. Math. Sci., http://dx.doi.org/10.1155/2009/630857.Google Scholar
• Glasserman P, Heidelberger P, Shahabuddin P (2000) Variance reduction techniques for estimating value-at-risk. Management Sci. 46(10):1349–1364.Link, Google Scholar
• Liu J (2012) Tail approximations of integrals of Gaussian random fields. Ann. Probab. 40(3):1069–1104.Crossref, Google Scholar
• Liu J, Xu G (2012) Some asymptotic results of Gaussian random fields with varying mean functions and the associated processes. Ann. Statist. 40(1):262–293.Crossref, Google Scholar
• Liu J, Xu G (2013) On the density functions of integrals of Gaussian random fields. Advances Appl. Probab. 45(2):398–424.Crossref, Google Scholar
• Liu J, Xu G (2014) On the conditional distributions and the efficient simulations of exponential integrals of Gaussian random fields. Ann. Appl. Probab. 24(4):1691–1738.Crossref, Google Scholar
• Tsirelson BS, Ibragimov IA, Sudakov VN (1976) Norms of Gaussian sample functions. Maruyama G, Prokhorov JV, eds. Proc. Third Japan–USSR Sympos. Probab. Theory, Lecture Notes in Mathematics, Vol. 550 (Springer, Berlin), 20–41.Crossref, Google Scholar
• Yor M (1992) On some exponential functionals of Brownian-motion. Advances Appl. Probab. 24(3):509–531.Crossref, Google Scholar