arXiv subjects

Lotfi Boudabsa

Publications and source records attributed to Lotfi Boudabsa.

4 recordsLinked to original sources

arXiv2022

Ensemble learning for portfolio valuation and risk management

We introduce an ensemble learning method for dynamic portfolio valuation and risk management building on regression trees. We learn the dynamic value process of a derivative portfolio from a finite sample of its cumulative cash flow. The estimator is given in closed form. The method is fast and accurate, and scales well with sample size and path space dimension. The method can also be applied to Bermudan style options. Numerical experiments show good results in moderate dimension problems.

q-fin.CP↗

arXiv2021

Machine learning with kernels for portfolio valuation and risk management

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.

q-fin.CP↗

arXiv2020

Some properties of the Kilbas-Saigo function

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le Roy function. The main ingredient for the proof is a probabilistic representation of these functions in terms of the stable subordinator.

math.CA↗

arXiv2019

Fractional extreme distributions

We consider three classes of linear differential equations on distribution functions, with a fractional order $α\in [0,1].$ The integer case $α=1$ corresponds to the three classical extreme families. In general, we show that there is a unique distribution function solving these equations, whose underlying random variable is expressed in terms of an exponential random variable and an integral transform of an independent $α-$stable subordinator. From the analytical viewpoint, this law is in one-to-one correspondence with a Kilbas-Saigo function for the Weibull and Fréchet cases, and with a Le Roy function for the Gumbel case. By the stochastic representation, we can derive several analytical properties for the latter special functions, extending known features of the classical Mittag-Leffler function, and dealing with monotonicity, complete monotonicity, infinite divisibility, asymptotic behaviour at infinity, uniform hyperbolic bounds.

math.PR↗