Salvador Ortiz-Latorre

• Benth, Fred Espen; Ortiz-Latorre, Salvador & Tarquini, Leonardo (2026). Signature McKean-Vlasov stochastic differential equations. arXiv. doi: 10.48550/ARXIV.2606.22964. Full text in Research Archive Show summary

  McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with $p\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chaos is established.

• Jolis, Maria; Ortiz-Latorre, Salvador & Quer-Sardanyons, Lluís (2026). Convergence in law for quasi-linear SPDEs. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. doi: 10.1007/s40072-026-00419-x. Full text in Research Archive Show summary

  We consider the quasi-linear stochastic wave and heat equations in $\mathbb{R}^d$ with $d\in \{1,2,3\}$ and $d\geq 1$, respectively, and perturbed by an additive Gaussian noise which is white in time and has a homogeneous spatial correlation with spectral measure $\mu_n$. We allow the Fourier transform of $\mu_n$ to be a genuine distribution. Let $u^n$ be the mild solution to these equations. We provide sufficient conditions on the measures $\mu_n$ and the initial data to ensure that $u^n$ converges in law, in the space of continuous functions, to the solution of our equations driven by a noise with spectral measure $\mu$, where $\mu_n\to\mu$ in some sense. We apply our main result to various types of noises, such as the anisotropic fractional noise. We also show that we cover existing results in the literature, such as the case of Riesz kernels and the fractional noise with $d=1$.

• Banos, David Ruiz; Ortiz-Latorre, Salvador & Font, Oriol Zamora (2026). A functional variational approach to pricing path dependent insurance policies. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN 1744-2508. p. 1–24. Full text in Research Archive Show summary

  The main purpose of this work is the derivation of a path-dependent partial differential equation for the calculations of equity-linked insurance policies, where the payment stream may depend on the whole past history of the financial asset. To this end, we employ variational techniques from the theory of functional Itô calculus.

• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2024). Change of measure in a Heston–Hawkes stochastic volatility model. Advances in Applied Probability. ISSN 0001-8678. 56, p. 1370–1399. doi: 10.1017/apr.2024.14. Full text in Research Archive Show summary

  We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance, insurance, epidemiology, seismology, and other fields. We prove a general result on the existence of a family of equivalent (local) martingale measures. We apply this result to a particular example where the sizes of the jumps are exponentially distributed. Finally, a practical application to efficient computation of exposures is discussed.

• Nunno, Giulia Di; Ortiz-Latorre, Salvador & Petersson, Andreas Erik (2023). SPDE bridges with observation noise and their spatial approximation. Stochastic Processes and their Applications. ISSN 0304-4149. 158, p. 170–207. doi: 10.1016/j.spa.2023.01.007. Full text in Research Archive Show summary

  This paper introduces SPDE bridges with observation noise and contains an analysis of their spatially semidiscrete approximations. The SPDEs are considered in the form of mild solutions in an abstract Hilbert space framework suitable for parabolic equations. They are assumed to be linear with additive noise in the form of a cylindrical Wiener process. The observational noise is also cylindrical and SPDE bridges are formulated via conditional distributions of Gaussian random variables in Hilbert spaces. A general framework for the spatial discretization of these bridge processes is introduced. Explicit convergence rates are derived for a spectral and a finite element based method. It is shown that for sufficiently rough observation noise, the rates are essentially the same as those of the corresponding discretization of the original SPDE.

• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2023). Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model. arXiv.org. ISSN 2331-8422. Full text in Research Archive
• Crisan, Dan; Lobbe, Alexander & Ortiz-Latorre, Salvador (2022). An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN 2194-0401. 10, p. 1050–1081. doi: 10.1007/s40072-022-00260-y. Full text in Research Archive Show summary

  Abstract The filtering equations govern the evolution of the conditional distribution of a signal process given partial, and possibly noisy, observations arriving sequentially in time. Their numerical approximation plays a central role in many real-life applications, including numerical weather prediction [Llopis et al. (SIAM J Sci Comput 40(3):A1544–A1565, 2018), Galanis et al. (Geophysicae 24(10): 2451–2460, 2006)], finance [Brigo and Hanzon (Insurance Math Econom 22(1):53–64, 1998), Date and Ponomareva (IMA J Manag Math 22(3): 195–211, 2011), Crisan and Rozovskii (The Oxford handbook of nonlinear filtering, 2011)] and engineering [Myötyri et al. (Reliability Eng Syst Saf 91(2):200–208, 2005)]. One of the classical approaches to approximate the solution of the filtering equations is to use a PDE inspired method, called the splitting-up method, initiated by Gyongy, Krylov, LeGland, among other contributors, see e.g., Gyöngy and Krylov (Stochastic inequalities and applications, Progr. Probab. 56:301–321, 2003), Le Gland(Stochastic partial differential equations and their applications (Charlotte, NC, 1991), Lect. Notes Control Inf. Sci. 176:177–187, 1992). This method, and other PDE based approaches, have particular applicability for solving low-dimensional problems. In this work we combine this method with a neural network representation inspired by [Han et al. (Proc Natl acad Sci 115(34):8505–8510, 2018)]. The new methodology is used to produce an approximation of the unnormalised conditional distribution of the signal process. We further develop a recursive normalisation procedure to recover the normalised conditional distribution of the signal process. The new scheme can be iterated over multiple time steps whilst keeping its asymptotic unbiasedness property intact. We test the neural network approximations with numerical approximation results for the Kalman and Benes filter.

• Crisan, Dan; Lobbe, Alexander & Ortiz-Latorre, Salvador (2022). Pathwise Approximations for the Solution of the Non-Linear Filtering Problem. In Yin, George & Zariphopoulou, Thaleia (Ed.), Stochastic Analysis, Filtering, and Stochastic Optimization - A Commemorative Volume to Honor Mark H. A. Davis’s Contributions. Springer Nature. ISSN 9783030985189. p. 79–99. doi: 10.1007/978-3-030-98519-6_4. Full text in Research Archive
• 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 Show summary

  In this paper, we prove the existence of strong solutions to an stochastic differential equation with a generalized drift driven by a multidimensional fractional Brownian motion for small Hurst parameters H<12. Here, the generalized drift is given as the local time of the unknown solution process, which can be considered an extension of the concept of a skew Brownian motion to the case of fractional Brownian motion. Our approach for the construction of strong solutions is new and relies on techniques from Malliavin calculus combined with a “local time variational calculus” argument.

• 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). 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 Show summary

  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 by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving 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 dependent on the self-exciting dynamics of the process. Moreover, we discuss various applications of this process, and give examples of different functions to model self-exciting behavior.

• Baños, David; Lagunas, Marc & Ortiz-Latorre, Salvador (2020). Variance and interest rate risk in unit-linked insurance policies. Risks. 8(3). doi: 10.3390/risks8030084. Full text in Research Archive Show summary

  One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.

• 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 Show summary

  The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of these functionals of arbitrary order. The result generalizes the classical work of Picard, who introduced first order discretizations to the filtering functionals. For a given time interval partition, we construct discretization schemes with convergence rates that are proportional with the m-power of the mesh of the partition for arbitrary m∈N. The result paves the way for constructing high order numerical approximation for the solution of the filtering problem.

• 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 Show summary

  For a commodity spot price dynamics given by an Ornstein–Uhlenbeck process with Barndorff-Nielsen–Shephard stochastic volatility, we price forward contracts using a new class of pricing measures, extending the classical Esscher transform, that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility.

• 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. 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. Full text in Research Archive
• 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 Show summary

  For a commodity spot price dynamics given by an Ornstein–Uhlenbeck (OU) process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium is derived in the case of arithmetic and geometric spot price processes, and it is demonstrated that we can provide flexible shapes that are typically observed in energy markets. In particular, our pricing measure preserves the affine model structure and decomposes into a price and volatility risk premium. In the geometric spot price model, we need to resort to a detailed analysis of a system of Riccati equations, for which we show existence and uniqueness of solution and asymptotic properties that explain the possible risk premium profiles. Among the typical shapes, the risk premium allows for a stochastic change of sign, and can attain positive values in the short end of the forward market and negative in the long end. Preprint of an article published in International Journal of Theoretical and Applied Finance 2015 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijtaf

• 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 Show summary

  We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Lévy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic splitting argument. The resulting error bound involves separate contributions of the compound Poisson approximation and of the discretization scheme for the Brownian part, and allows, on one hand, to balance the two contributions in order to minimize the computational time, and on the other hand, to study the optimal design of the approximating compound Poisson process. For driving processes whose Lévy measure explodes near zero in a regularly varying way, this procedure allows us to construct discretization schemes with arbitrary order of convergence for sufficiently regular functionals. Definitive version available at ams.org © 2013 American Mathematical Society

• Benth, Fred Espen & Ortiz-Latorre, Salvador (2014). A pricing measure to explain the risk premium in power markets. SIAM Journal on Financial Mathematics. 5, p. 685–728. doi: 10.1137/13093604X. Full text in Research Archive Show summary

  In electricity markets, it is sensible to use a two-factor model with mean reversion for spot prices. One of the factors is an Ornstein–Uhlenbeck (OU) process driven by a Brownian motion and accounts for the small variations. The other factor is an OU process driven by a pure jump L´evy process and models the characteristic spikes observed in such markets. When it comes to pricing, a popular choice of pricing measure is given by the Esscher transform that preserves the probabilistic structure of the driving L´evy processes while changing the levels of mean reversion. Using this choice one can generate stochastic risk premiums (in geometric spot models) but with (deterministically) changing sign. In this paper we introduce a pricing change of measure, which is an extension of the Esscher transform. With this new change of measure we can also slow down the speed of mean reversion and generate stochastic risk premiums with stochastic nonconstant sign, even in arithmetic spot models. In particular, we can generate risk profiles with positive values in the short end of the forward curve and negative values in the long end. Finally, our pricing measure allows us to have a stationary spot dynamics while still having randomly fluctuating forward prices for contracts far from maturity. © 2014 Society for Industrial and Applied Mathematics

• 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 Show summary

  The aim of this paper is to introduce a new numerical algorithm for solving the continuous time nonlinear filtering problem. In particular, we present a particle filter that combines the Kusuoka–Lyons–Victoir (KLV) cubature method on Wiener space to approximate the law of the signal with a minimal variance ‘thinning’ method, called the tree-based branching algorithm (TBBA) to keep the size of the cubature tree constant in time. The novelty of our approach resides in the adaptation of the TBBA algorithm to simultaneously control the computational effort and incorporate the observation data into the system. We provide the rate of convergence of the approximating particle filter in terms of the computational effort (number of particles) and the discretization grid mesh. Finally, we test the performance of the new algorithm on a benchmark problem (the Beneš filter).

• 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. 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 9789814355704. p. 3–26. doi: 10.1142/9789814355711_0001. Full text in Research Archive
• Kohatsu-Higa, Arturo & Ortiz-Latorre, Salvador (2010). Weak Kyle-Back equilibrium models for Max and ArgMax. SIAM Journal on Financial Mathematics. 1(1), p. 179–211. doi: 10.1137/080739768. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive

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• Ortiz-Latorre, Salvador (2026). Heston-Hawkes stochastic volatility model: Change of measure and Thiele's PIDE. Full text in Research Archive
• Ortiz-Latorre, Salvador (2026). Convergence in law for quasi-linear SPDEs. Full text in Research Archive
• Ortiz-Latorre, Salvador (2025). Robustness of quasi-linear SPDEs with respect to the driving noise. Full text in Research Archive
• Ortiz-Latorre, Salvador (2024). Deep learning methods for the stochastic filtering problem. Full text in Research Archive
• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes Stochastic Volatility Model: Change of Measure and Forward Variance. Full text in Research Archive
• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes stochastic volatility model: change of measure and forward variance. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Strong solutions for singular SDEs driven by fractional Brownian motion. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Pathwise approximations for the solution of the non-linear filtering problem. Full text in Research Archive
• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2023). Change of measure in a Heston-Hawkes stochastic volatility model. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). SPDE bridges with observation noise and their spatial approximation. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Strong solutions for singular SDEs driven by fractional Brownian motion. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Time discretizations for the nonlinear filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Robust approximations for the solution of the non-linear filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2023). Robust discretizations for the solution of the non-linear filtering problem. Full text in Research Archive
• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2023). Heston-Hawkes stochastic volatility model: Change of measure and Thiele's PIDE. Full text in Research Archive
• Ortiz-Latorre, Salvador (2022). Deep learning methods for the stochastic filtering problem. Full text in Research Archive
• Font, Oriol Zamora; Baños, David & Ortiz-Latorre, Salvador (2022). Change of measure in a Heston-Hawkes stochastic volatility model. Full text in Research Archive
• Ortiz-Latorre, Salvador (2022). Machine learning applied to the stochastic filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2022). High order discretizations to the nonlinear filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador & Crisan, Dan (2020). High order discretizations to the nonlinear filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador & Lagunas, Marc (2019). A Hull-White Formula for a Fractional Volatility Lévy Model. Full text in Research Archive
• Merino, Marc Lagunas; Harang, Fabian Andsem & Ortiz-Latorre, Salvador (2019). Self-Exciting Multifractional Processes (SEM) Processes. Full text in Research Archive 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 (2019). High order discretizations to the nonlinear filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador & Crisan, Dan (2018). High order discretizations to the nonlinear filtering problem. Full text in Research Archive
• 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. Full text in Research Archive
• Ortiz-Latorre, Salvador (2016). High Order Weak Approximation of SDEs. Application to the Nonlinear Filtering Problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2016). High Order Discretizations to the Stochastic Filtering Problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2016). A second order approximation of the continuous time filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2016). A new pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2015). A Pricing measure for non-tradable assets with mean-reverting dynamics. Full text in Research Archive
• Ortiz-Latorre, Salvador (2015). A change of measure preserving the affine structure in the BNS model for commodity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2015). A new pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2015). A new flexible pricing measure in the Barndorff-Nielsen & Shephard model for commodity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2014). On a new pricing measure in electricity and commodity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2014). Speeding up and slowing down in the risk neutral world. A new flexible pricing measure for mean reverting models. Full text in Research Archive
• Ortiz-Latorre, Salvador (2013). A pricing measure to explain the risk premium in power markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2013). A second order approximation of the continuous time filtering problem. Full text in Research Archive
• Latorre, Salvador Ortiz (2013). A second order approximation to the continuous time filtering problem. Full text in Research Archive
• Latorre, Salvador Ortiz (2013). A pricing measure to explain risk premium in power markets. Full text in Research Archive
• Latorre, Salvador Ortiz (2013). Stochastic modeling of electricity markets. Full text in Research Archive
• Ortiz-Latorre, Salvador (2012). A second order approximation of the continuous time filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2012). A new approximation algorithm to solve the filtering problem combining Cubature and TBBA. Full text in Research Archive
• Ortiz-Latorre, Salvador (2012). A second order approximation of the continuous time filtering problem. Full text in Research Archive
• Ortiz-Latorre, Salvador (2012). Optimal simulation schemes for Lévy driven SDEs. Full text in Research Archive
• Ortiz-Latorre, Salvador (2012). Optimal simulation schemes for Lévy driven SDEs. 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 9789814355704. doi: 10.1142/9789814355711_0001. Full text in Research Archive
• Ortiz-Latorre, Salvador (2011). Weak Kyle-Back equilibrium models. Full text in Research Archive
• Ortiz-Latorre, Salvador (2011). Weak convergence of nonlinear functionals of Gaussian processes and Malliavin calculus. Full text in Research Archive
• Ortiz-Latorre, Salvador (2011). A new approximation algorithm to solve the filtering problem combining Cubature and TBBA. Full text in Research Archive
• Ortiz-Latorre, Salvador (2011). Weak Kyle-Back equilibrium models. Full text in Research Archive
• Ortiz-Latorre, Salvador (2009). Stein's method and Malliavin calculus. Full text in Research Archive
• Ortiz-Latorre, Salvador (2009). An introduction to Stein's method. Full text in Research Archive
• Ortiz-Latorre, Salvador (2009). An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach. Full text in Research Archive
• Ortiz-Latorre, Salvador (2009). An Itô-Stratonovich formula for Gaussian processes: A Riemann sums approach. Full text in Research Archive
• Ortiz-Latorre, Salvador (2007). Central limit theorems for multiple stochastic integrals and Malliavin calculus. Full text in Research Archive
• Lozano, Pere Diaz; Nunno, Giulia Di & Ortiz-Latorre, Salvador (2026). Backward stochastic equations and martingale modelling. Universitetet i Oslo. Full text in Research Archive Show summary

  This thesis is concerned with numerical methods and regularity properties for backward stochastic equations, together with martingale modelling in mathematical finance. The main tools are Wiener chaos expansions and Malliavin calculus. The first part focuses on backward stochastic differential equations (BSDEs). We develop numerical methods that do not require the terminal condition to be given as a function of a forward diffusion, as is often assumed in the literature. Instead, the terminal condition is represented through its Wiener chaos expansion. This leads to two related approaches: an operator-based Euler scheme that approximates the map sending terminal conditions to BSDE solutions, and a chaos-based Euler scheme in which conditional expectations and martingale integrands are computed through finite chaos projections. Convergence results are obtained for both methods. In the second part, we apply the same Wiener chaos point of view to financial modelling. Starting from the no-arbitrage requirement that discounted prices should be martingales under a risk-neutral measure, we construct an over-parameterized square-integrable martingale model by parameterizing its terminal value through a finite Wiener chaos expansion. The resulting model is arbitrage-free by construction, dense in the space of square-integrable martingales, and can be efficiently calibrated to implied volatility surfaces. The final part of the thesis studies backward stochastic Volterra integral equations (BSVIEs). We establish Hölder-type regularity estimates for the martingale integrand, both for the original BSVIE and for a system of approximating BSDEs. These estimates are then used to prove a convergence rate for an explicit Euler-type approximation of the BSVIE.

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