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A BSDE with delayed generator approach to pricing under counterparty risk and collateralization
We consider a nonlinear pricing problem that takes into account credit risk and funding
issues. The aforementioned problem is formulated as a stochastic forward‐backward system …
issues. The aforementioned problem is formulated as a stochastic forward‐backward system …
A probabilistic method for a class of non-Lipschitz BSDEs with application to fund management
The present work is devoted to a study of the solvability of a class of non-Lipschitz and
noncanonical backward stochastic differential equations (BSDEs) that naturally arises from …
noncanonical backward stochastic differential equations (BSDEs) that naturally arises from …
A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps
We consider a stochastic functional delay differential equation, namely an equation whose
evolution depends on its past history as well as on its present state, driven by a pure …
evolution depends on its past history as well as on its present state, driven by a pure …
Stochastic Maximum Principle for Optimal Liquidation with Control-Dependent Terminal Time
In this paper we study a general optimal liquidation problem with a control-dependent
stop** time which is the first time the stock holding becomes zero or a fixed terminal time …
stop** time which is the first time the stock holding becomes zero or a fixed terminal time …
Semilinear Kolmogorov equations on the space of continuous functions via BSDEs
We deal with a class of semilinear parabolic PDEs on the space of continuous functions that
arise, for example, as Kolmogorov equations associated to the infinite-dimensional lifting of …
arise, for example, as Kolmogorov equations associated to the infinite-dimensional lifting of …
Feynman–Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations
We consider a system of forward backward stochastic differential equations (FBSDEs) with a
time-delayed generator driven by Lévy-type noise. We establish a non-linear Feynman–Kac …
time-delayed generator driven by Lévy-type noise. We establish a non-linear Feynman–Kac …
SDEs and MFGs towards Machine Learning applications
M Garbelli - 2023 - tesidottorato.depositolegale.it
We present results that span three interconnected domains. Initially, our analysis is centred
on Backward Stochastic Differential Equations (BSDEs) featuring time-delayed generators …
on Backward Stochastic Differential Equations (BSDEs) featuring time-delayed generators …
[HTML][HTML] Time-delayed generalized BSDEs
We prove the existence and uniqueness of the solution of a BSDE with time-delayed
generators in the small delay setting (or equivalently small Lipschitz constant), which …
generators in the small delay setting (or equivalently small Lipschitz constant), which …
BSDEs and SDEs with time-advanced and-delayed coefficients
This paper introduces a class of backward stochastic differential equations (BSDEs), whose
coefficients not only depend on the value of its solutions of the present but also the past and …
coefficients not only depend on the value of its solutions of the present but also the past and …
Portfolio optimization in presence of a self-exciting jump process: from theory to practice
A Veronese - 2022 - tesidottorato.depositolegale.it
We aim at generalizing the celebrated portfolio optimization problem" à la Merton", where
the asset evolution is steered by a self-exciting jump-diffusion process. We first define the …
the asset evolution is steered by a self-exciting jump-diffusion process. We first define the …