Salvador Ortiz-Latorre

• Baños, David; Ortiz-Latorre, Salvador; Pilipenko, Andrey & Proske, Frank Norbert (2021). Strong Solutions of Stochastic Differential Equations with Generalized Drift and Multidimensional Fractional Brownian Initial Noise. Journal of theoretical probability. ISSN 0894-9840. doi: 10.1007/s10959-021-01084-7. Full text in Research Archive
• Crisan, Dan; Kurtz, Thomas G. & Ortiz-Latorre, Salvador (2021). Particle Representation for the Solution of the Filtering Problem. Application to the Error Expansion of Filtering Discretizations. Journal of Stochastic Analysis (JOSA). ISSN 2689-6931. doi: 10.31390/josa.2.3.15. Full text in Research Archive Show summary

  We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In this paper, we explore some of its theoretical con- sequences. The first is to deduce the equations satisfied by the solution of the filtering problem in three different frameworks: the signal independent Brownian measurement noise model, the spatial observations with additive white noise model and the cluster detection model in spatial point processes. Secondly we use the representation to show that a suitably chosen filtering discretisation converges to the filtering solution. Thirdly we study the leading error coefficient for the discretisation. We show that it satisfies a stochastic partial differential equation by exploiting the weighted particle representation for both the approximation and the limiting filtering solution.

• Harang, Fabian Andsem; Lagunas, Marc & Ortiz-Latorre, Salvador (2021). Self-Exciting Multifractional Processes. Journal of Applied Probability. ISSN 0021-9002. 58(1), p. 22–41. doi: 10.1017/jpr.2020.88. Full text in Research Archive
• 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
• Crisan, Dan & Ortiz-Latorre, Salvador (2019). A high order time discretization of the solution of the non-linear filtering problem. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. p. 1–68. doi: 10.1007/s40072-019-00157-3. Full text in Research Archive
• Crisan, Dan & Ortiz-Latorre, Salvador (2017). A high order time discretization of the solution of the non-linear filtering problem. arXiv.org. ISSN 2331-8422. doi: 10.1007/s40072-019-00157-3.
• Ortiz-Latorre, Salvador (2017). A new pricing measure in the Barndorff-Nielsen?Shephard model for commodity markets. Trends in Mathematics. ISSN 2297-0215. 6, p. 133–139. doi: 10.1007/978-3-319-51753-7_22. Full text in Research Archive
• Benth, Fred Espen & Ortiz-Latorre, Salvador (2017). Calibration of temperature futures by changing the mean reversion. Journal of Energy Markets. ISSN 1756-3607. 10(1), p. 1–25. doi: 10.21314/jem.2017.157.
• Benth, Fred Espen & Ortiz-Latorre, Salvador (2015). A change of measure preserving the affine structure in the Barndorff-Nielsen and Shephard model for commodity markets. International Journal of Theoretical and Applied Finance. ISSN 0219-0249. 18(6). doi: 10.1142/S0219024915500387. Full text in Research Archive
• Benth, Fred Espen & Ortiz-Latorre, Salvador (2014). A pricing measure to explain the risk premium in power markets. SIAM Journal on Financial Mathematics. ISSN 1945-497X. 5, p. 685–728. doi: 10.1137/13093604X. Full text in Research Archive
• Kohatsu-Higa, Arturo; Ortiz-Latorre, Salvador & Tankov, Peter (2014). Optimal simulation schemes for Lévy driven stochastic differential equations. Mathematics of Computation. ISSN 0025-5718. 83(289), p. 2293–2324. doi: 10.1090/S0025-5718-2013-02786-X. Full text in Research Archive
• Crisan, Dan & Ortiz-Latorre, Salvador (2013). A Kusuoka-Lyons-Victoir particle filter. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. ISSN 1364-5021. 469(2156). doi: 10.1098/rspa.2013.0076. Full text in Research Archive
• Nualart, David & Ortiz-Latorre, Salvador (2011). Multidimensional Wick–Itô Formula for Gaussian Processes. In Tsoi, Allan; Nualart, David & Yin, George (Ed.), Stochastic Analysis, Stochastic Systems, and Applications to Finance. World Scientific. ISSN 978-981-4355-70-4. p. 3–26. doi: 10.1142/9789814355711_0001.
• Kohatsu-Higa, Arturo & Ortiz-Latorre, Salvador (2011). Modelling of financial markets with inside information in continuous time. Stochastics and Dynamics. ISSN 0219-4937. 11(2-3). doi: 10.1142/S0219493711003371.
• Kohatsu-Higa, Arturo & Ortiz-Latorre, Salvador (2010). Weak Kyle-Back equilibrium models for Max and ArgMax. SIAM Journal on Financial Mathematics. ISSN 1945-497X. 1(1), p. 179–211. doi: 10.1137/080739768.
• Nualart, David & Ortiz-Latorre, Salvador (2008). An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach. Stochastic Processes and their Applications. ISSN 0304-4149. 118(10), p. 1803–1819. doi: 10.1016/j.spa.2007.11.002.
• Nualart, David & Ortiz-Latorre, Salvador (2008). Central limit theorems for multiple stochastic integrals and Malliavin calculus. Stochastic Processes and their Applications. ISSN 0304-4149. 118(4), p. 614–628. doi: 10.1016/j.spa.2007.05.004.
• Nualart, David & Ortiz-Latorre, Salvador (2007). Intersection local time for two independent fractional Brownian motions. Journal of theoretical probability. ISSN 0894-9840. 20(4), p. 759–767. doi: 10.1007/s10959-007-0106-x.

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• Ortiz-Latorre, Salvador & Crisan, Dan (2020). High order discretizations to the nonlinear filtering problem.
• Ortiz-Latorre, Salvador & Lagunas, Marc (2019). A Hull-White Formula for a Fractional Volatility Lévy Model.
• Ortiz-Latorre, Salvador & Crisan, Dan (2019). High order discretizations to the nonlinear filtering problem.
• Lagunas Merino, Marc; Harang, Fabian Andsem & Ortiz-Latorre, Salvador (2019). Self-Exciting Multifractional Processes (SEM) Processes. Show summary

  Abstract. We propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this through a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as give bounds on the p-order moments, for all p>=1. We show convergence of an Euler-Maruyama scheme for the process, and also give the rate of convergence, which is depending on the self-exciting dynamics of the process. Moreover, we discuss different applications of this process, and give examples of different functions to model self-exciting behavior.

• Ortiz-Latorre, Salvador & Crisan, Dan (2018). High order discretizations to the nonlinear filtering problem.
• 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.
• Ortiz-Latorre, Salvador (2016). High Order Discretizations to the Stochastic Filtering Problem.
• Ortiz-Latorre, Salvador (2016). A new pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets.
• Ortiz-Latorre, Salvador (2016). A second order approximation of the continuous time filtering problem.
• Ortiz-Latorre, Salvador (2016). High Order Weak Approximation of SDEs. Application to the Nonlinear Filtering Problem.
• Ortiz-Latorre, Salvador (2015). A Pricing measure for non-tradable assets with mean-reverting dynamics.
• Ortiz-Latorre, Salvador (2015). A new pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets.
• Ortiz-Latorre, Salvador (2015). A new flexible pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets.
• Ortiz-Latorre, Salvador (2015). A change of measure preserving the affine structure in the BNS model for commodity markets.
• Ortiz-Latorre, Salvador (2014). Speeding up and slowing down in the risk neutral world. A new flexible pricing measure for mean reverting models.
• Ortiz-Latorre, Salvador (2014). On a new pricing measure in electricity and commodity markets.
• Ortiz-Latorre, Salvador (2013). A second order approximation of the continuous time filtering problem.
• Ortiz-Latorre, Salvador (2013). A pricing measure to explain the risk premium in power markets.
• Ortiz Latorre, Salvador (2013). A pricing measure to explain risk premium in power markets.
• Ortiz Latorre, Salvador (2013). Stochastic modeling of electricity markets.
• Ortiz Latorre, Salvador (2013). A second order approximation to the continuous time filtering problem.
• Ortiz-Latorre, Salvador (2012). A second order approximation of the continuous time filtering problem.
• Ortiz-Latorre, Salvador (2012). Optimal simulation schemes for Lévy driven SDEs.
• Ortiz-Latorre, Salvador (2012). Optimal simulation schemes for Lévy driven SDEs.
• Ortiz-Latorre, Salvador (2012). A new approximation algorithm to solve the filtering problem combining Cubature and TBBA.
• Ortiz-Latorre, Salvador (2012). A second order approximation of the continuous time filtering problem.
• Ortiz-Latorre, Salvador (2011). A new approximation algorithm to solve the filtering problem combining Cubature and TBBA.
• Ortiz-Latorre, Salvador (2011). Weak Kyle-Back equilibrium models.
• Ortiz-Latorre, Salvador (2011). Weak Kyle-Back equilibrium models.
• Ortiz-Latorre, Salvador (2011). Weak convergence of nonlinear functionals of Gaussian processes and Malliavin calculus.
• Ortiz-Latorre, Salvador (2009). An introduction to Stein's method.
• Ortiz-Latorre, Salvador (2009). An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach.
• Ortiz-Latorre, Salvador (2009). An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach.
• Ortiz-Latorre, Salvador (2009). Stein's method and Malliavin calculus.
• Ortiz-Latorre, Salvador (2007). Central limit theorems for multiple stochastic integrals and Malliavin calculus.

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