David Ruiz Baños

• Amine, Oussama; Baños, David & Proske, Frank Norbert (2020). Regularity properties of the stochastic flow of a skew fractional Brownian motion. Infinite Dimensional Analysis Quantum Probability and Related Topics.  ISSN 0219-0257.  23(1) . doi: 10.1142/S0219025720500058
• Baños, David; Lagunas, Marc & Ortiz-Latorre, Salvador (2020). Variance and interest rate risk in unit-linked insurance policies. Risks.  ISSN 2227-9091.  8(3) . doi: 10.3390/risks8030084 Full text in Research Archive.
• Baños, David Ruiz; Nilssen, Torstein Kastberg & Proske, Frank Norbert (2019). Strong Existence and Higher Order Fréchet Differentiability of Stochastic Flows of Fractional Brownian Motion Driven SDEs with Singular Drift. Journal of Dynamics and Differential Equations.  ISSN 1040-7294.  32, s 1819- 1866 . doi: 10.1007/s10884-019-09789-4 Full text in Research Archive. Show summary

  In this paper we present a new method for the construction of strong solutions of SDE’s with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter H<1/2. Furthermore, we prove the rather surprising result of the higher order Fréchet differentiability of stochastic flows of such SDE’s in the case of a small Hurst parameter. In establishing these results we use techniques from Malliavin calculus combined with new ideas based on a “local time variational calculus”. We expect that our general approach can be also applied to the study of certain types of stochastic partial differential equations as e.g. stochastic conservation laws driven by rough paths.

• Baños, David; Bauer, Martin; Meyer-Brandis, Thilo & Proske, Frank Norbert (2019). Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise. arXiv.org.  ISSN 2331-8422. Full text in Research Archive.
• Banos, David; Bølviken, Erik; Duedahl, Sindre & Proske, Frank Norbert (2019). Modeling and estimation of stochastic transition rates in life insurance with regime switching based on generalized Cox processes. Scandinavian Actuarial Journal.  ISSN 0346-1238. . doi: 10.1080/03461238.2019.1636858 Full text in Research Archive. Show summary

  In this paper we aim at modeling stochastic transition rates of state processes in life insurance by using generalized Cox processes. A feature of a our non-Gaussian model is that it can be used to capture ‘regime switching’ effects of data which may be due to regulatory changes in insurance markets or external ‘shocks’ caused e.g. by an economical crisis, natural disasters or epidemics. We propose a method how to estimate the unknown parameters of our model for stochastic transition rates from insurance data by using non-linear filtering techniques for Lévy processes. As a result we also obtain an explicit formula for the unnormalized density of a filtering problem with singular coefficients.

• Banos, David; Cordoni, Francesco; Di Nunno, Giulia; Di Persio, Luca & Røse, Elin Engen (2019). Stochastic systems with memory and jumps. Journal of Differential Equations.  ISSN 0022-0396.  266(9), s 5772- 5820 . doi: http://dx.doi.org/10.1016/j.jde.2018.10.052 Full text in Research Archive.
• Amine, Oussama; Banos, David & Proske, Frank Norbert (2018). Regularity Properties of the Stochastic Flow of a Skew Fractional Brownian Motion. arXiv.org.  ISSN 2331-8422. . doi: 10.1142/s0219025720500058
• Baños, David Ruiz (2018). The Bismut-Elworthy-Li formula for mean-field stochastic differential equations. Annales de l'I.H.P. Probabilites et statistiques.  ISSN 0246-0203.  54(1), s 220- 233 . doi: 10.1214/16-AIHP801
• Baños, David Ruiz; Duedahl, Sindre; Meyer-Brandis, Thilo & Proske, Frank Norbert (2018). Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle. Annales de l'I.H.P. Probabilites et statistiques.  ISSN 0246-0203.  54(3), s 1464- 1491 . doi: 10.1214/17-AIHP845 Full text in Research Archive.
• Baños, David; Di Nunno, Giulia; Haferkorn, Hannes Hagen & Proske, Frank Norbert (2018). Stochastic functional differential equations and sensitivity to their initial path, In Elena Celledoni; Giulia Di Nunno; Kurusch Ebrahimi-Fard & Hans Munthe-Kaas (ed.),  Computation and Combinatorics in Dynamics, Stochastics and Control.  Springer.  ISBN 978-3-030-01592-3.  2.  s 37 - 70
• Baños, David Ruiz; Haferkorn, Hannes Hagen & Proske, Frank Norbert (2017). Strong Uniqueness of Singular Stochastic Delay Equations. arXiv.org.  ISSN 2331-8422.
• Baños, David Ruiz & Krühner, Paul (2017). Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients. Stochastic Processes and their Applications.  ISSN 0304-4149.  127(6), s 1785- 1799 . doi: 10.1016/j.spa.2016.09.015
• Baños, David Ruiz; Meyer-Brandis, Thilo; Proske, Frank Norbert & Duedahl, Sindre (2017). Computing Deltas without Derivatives. Finance and Stochastics.  ISSN 0949-2984.  21(2), s 509- 549 . doi: 10.1007/s00780-016-0321-3 Full text in Research Archive.
• Baños, David Ruiz; Ortiz-Latorre, Salvador; Pilipenko, Andrey & Proske, Frank Norbert (2017). Strong solutions of d-dimensional SDE's with generalized drift and fractional Brownian initial noise. arXiv.org.  ISSN 2331-8422. . doi: https://arxiv.org/abs/1705.01616 Full text in Research Archive.
• Baños, David Ruiz & Proske, Frank Norbert (2017). C-infinity-regularization by Noise of Singular ODE's. arXiv.org.  ISSN 2331-8422. . doi: arXiv:1710.05760[math.FA] Full text in Research Archive.
• Baños, David Ruiz & Krühner, Paul (2016). Optimal density bounds for marginals of Itô processes. Communications on Stochastic Analysis.  ISSN 0973-9599.  10(2), s 131- 150 . doi: 10.31390/cosa.10.2.01
• Baños, David Ruiz & Nilssen, Torstein Kastberg (2016). Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation. Stochastics: An International Journal of Probability and Stochastic Processes.  ISSN 1744-2508.  88(4), s 540- 566 . doi: 10.1080/17442508.2015.1102265

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• Baños, David Ruiz; Ortiz-Latorre, Salvador; Pilipenko, Andrey & Proske, Frank Norbert (2017). Strong solutions of SDE's with generalized drift and multidimensional fractional Brownian initial noise.
• Nilssen, Torstein Kastberg; Baños, David Ruiz & Proske, Frank Norbert (2016). Strong Existence and higher order differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift.

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