scholarly journals Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales

2021 ◽  
Vol 6 (4) ◽  
pp. 319
Author(s):  
Tianyang Nie ◽  
Marek Rutkowski
Keyword(s):  
Brownian Motion ◽  
Financial Models ◽  
Wide Spectrum ◽  
Comparison Theorems ◽  
One Dimensional ◽  
Non Linear

<p style='text-indent:20px;'>The existence, uniqueness, and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed. The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps, including as particular cases, the setups studied by Peng and Xu [<xref ref-type="bibr" rid="b27">27</xref>, <xref ref-type="bibr" rid="b28">28</xref>] and Dumitrescu et al. [<xref ref-type="bibr" rid="b7">7</xref>] who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. </p>

Reflected and doubly reflected BSDEs driven by RCLL martingales

2021 ◽  
Author(s):  
Tianyang Nie ◽  
Marek Rutkowski
Keyword(s):  
Brownian Motion ◽  
Default Risk ◽  
Financial Models ◽  
Wide Spectrum ◽  
Random Measure ◽  
One Dimensional ◽  
Default Time ◽  
Working Paper ◽  
And Control ◽  
Reflected Bsdes

We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu [BSDEs with random default time and their applications to default risk, working paper, preprint (2009), arXiv:0910.2091] and Dumitrescu et al. [BSDEs with default jump, in Computation and Combinatorics in Dynamics, Stochastics and Control, Abel Symposia, Vol. 13, eds. E. Celledoni, G. Di Nunno, K. Ebrahimi-Fard and H. Munthe-Kaas (Springer, Cham, 2018), pp. 233–263] who examined BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.

scholarly journals Interaction of equivalence ratio fluctuations and flow fluctuations in acoustically forced swirl flames

2021 ◽  
pp. 175682772110155
Author(s):  
Vincent Kather ◽  
Finn Lückoff ◽  
Christian O. Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Equivalence Ratio ◽  
Transfer Functions ◽  
Transport Model ◽  
Mode Conversion ◽  
Fuel Injector ◽  
One Dimensional ◽  
Flow Fluctuations ◽  
Non Linear ◽  
Non Local ◽  
Acoustic Forcing

The generation and turbulent transport of temporal equivalence ratio fluctuations in a swirl combustor are experimentally investigated and compared to a one-dimensional transport model. These fluctuations are generated by acoustic perturbations at the fuel injector and play a crucial role in the feedback loop leading to thermoacoustic instabilities. The focus of this investigation lies on the interplay between fuel fluctuations and coherent vortical structures that are both affected by the acoustic forcing. To this end, optical diagnostics are applied inside the mixing duct and in the combustion chamber, housing a turbulent swirl flame. The flame was acoustically perturbed to obtain phase-averaged spatially resolved flow and equivalence ratio fluctuations, which allow the determination of flux-based local and global mixing transfer functions. Measurements show that the mode-conversion model that predicts the generation of equivalence ratio fluctuations at the injector holds for linear acoustic forcing amplitudes, but it fails for non-linear amplitudes. The global (radially integrated) transport of fuel fluctuations from the injector to the flame is reasonably well approximated by a one-dimensional transport model with an effective diffusivity that accounts for turbulent diffusion and dispersion. This approach however, fails to recover critical details of the mixing transfer function, which is caused by non-local interaction of flow and fuel fluctuations. This effect becomes even more pronounced for non-linear forcing amplitudes where strong coherent fluctuations induce a non-trivial frequency dependence of the mixing process. The mechanisms resolved in this study suggest that non-local interference of fuel fluctuations and coherent flow fluctuations is significant for the transport of global equivalence ratio fluctuations at linear acoustic amplitudes and crucial for non-linear amplitudes. To improve future predictions and facilitate a satisfactory modelling, a non-local, two-dimensional approach is necessary.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

scholarly journals BSDEs with Logarithmic Growth Driven by Brownian Motion and Poisson Random Measure and Connection to Stochastic Control Problem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid Oufdil
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Random Measure ◽  
Poisson Random Measure ◽  
One Dimensional ◽  
Stochastic Optimal Control Problem ◽  
Uniqueness Of The Solution ◽  
Logarithmic Growth

Abstract In this paper, we study one-dimensional backward stochastic differential equations under logarithmic growth in the 𝑧-variable ( | z | ⁢ | ln ⁡ | z | | ) (\lvert z\rvert\sqrt{\lvert\ln\lvert z\rvert\rvert}) . We show the existence and the uniqueness of the solution when the noise is driven by a Brownian motion and an independent Poisson random measure. In addition, we highlight the connection of such BSDEs with stochastic optimal control problem, where we show the existence of an optimal strategy for the control problem.

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