Łukasz Delong SGH

Łukasz Delong

University of Warsaw Faculty of Economic Sciences Department of Statistics and Econometrics

I work as a Full Professor at the Faculty of Economic Sciences at University of Warsaw. I have PhD in Mathematics, Habilitation Degree in Economics and Professor title in Economics and Finance. I am an actuary with license no. 130 issued by the Polish Financial Supervision Authority, the Head of the Examination Committee for Actuaries at the Polish Financial Supervision Authority and a Board Member of the Polish Society of Actuaries. My scientific research includes different areas of actuarial mathematics with emphasis on stochastic modelling of financial risks and actuarial statistical learning. I am an Editor of ASTIN Bulletin – The Journal of International Actuarial Association.


01.02.2024 – Read new versions of papers about istotonic regresion for variance modelling and one-year vs ultimate correlations

01.10.2023 – I moved to University of Warsaw and took a new position of full professor at Faculty of Economic Sciences. My new e-mail: l.delong@uw.edu.pl

01.05.2022 – Together with Mathias Lindholm and Mario Wüthrich, we received Gauss Prize for the best paper published in EAJ

  • December

    Title of Professor in Economics and Finance, Conferred by the President of the Republic of Poland upon a motion of The Council of Scientific Excellence

    Promoted based on scientific and didactic achievements under the Higher Education and Science Law

  • May 2013

    Habilitation Degree in Economics, SGH Warsaw School of Economics, Collegium of Economic Analysis

    Promoted based on a series of publications on Applications of Backward Stochastic Differential Equations to Insurance and Finance

  • October

    Doctor of Philosophy in Mathematics, Institute of Mathematics, Polish Academy of Sciences

    PhD thesis: Optimal investment strategies in financial markets driven by a Lévy process, with applications to insurance

    Supervised by Professor Łukasz Stettner (IM PAN)

    Defended with distinction

  • 1999-2003

    Master of Arts in Economics, SGH Warsaw School of Economics, Quantitative Methods and Information Systems

    Diploma thesis: Ruin probabilities under force of interest

    Supervised by Professor Agata Boratyńska (SGH)

    Graduated with honours

Read more
Łukasz Delong SGH


Actuarial Mathematics

I deal with various topics from actuarial mathematics...

During my research and teaching work, I deal with various topics from actuarial mathematics. I have strong background in risk measures, loss distributions, dependence modelling with copulas and claims reserving methods. I am familiar with statistical methods and probabilistic properties of actuarial models.

Financial Mathematics

Financial mathematics inspired my first research...

Although I was educated in actuarial science, financial mathematics inspired my first research. I have deep knowledge of stochastic models for equity, volatility and interest rate used for pricing derivatives. I have experience in Monte Carlo methods and Least Square Monte Carlo methods.

Actuarial and Financial Practice

I have an opportunity to apply and validate theoretical models in practice...

While working as an expert for insurance industry I have an opportunity to apply and validate theoretical models in practice. During the last years I was involved in providing expertise concerning models and methods for Solvency II, IFRS 17, non-life claims reserving, non-life ratemaking, loss distributions, dependence modelling, Monte Carlo simulations and pricing of derivatives (embedded financial options).

HJBs and BSDEs

My primary research focuses on stochastic optimal control theory...

My primary research focuses on stochastic optimal control theory. I solve dynamic optimization problem which we face when trying to hedge financial and insurance claims and find optimal strategies. I specialize in Hamilton-Jacobi-Bellman equations and Backward Stochastic Differential Equations.

Lévy processes

Jumps are important in insurance and financial models...

“The more we jump – the more we get – if not more quality, then at least more variety” – Lévy Processes and Stochastic Calculus by D. Applebaum and Faster by J. Gleick.


Jumps are important in insurance and financial models and they do add quality. I have strong background in stochastic calculus for jump process, their theoretical properties and financial/insurance applications.

From GLMs to Neural Networks

Non-life ratemaking, loss distribution modeling, individual claims reserving and BSDEs solvers...

I have deep knowledge and experience in applying Generalized Linear Models, Generalized Additive Models, trees and neural networks in actuarial and non-actuarial applications, including non-life ratemaking, loss distribution modeling, individual claims reserving and solving backward stochastic differential equations. My research has switched to applications of machine learning techniques to actuarial statistical problems and optimal control problems.

Delong, Ł., Wüthrich, 2024, Isotonic regression for variance estimation and its role in mean estimation and model validation

Working Paper, 01-07-2023

We study isotonic regression which is a non-parametric rank-preserving regression technique. Under the assumption that the variance function of a response is monotone in its mean functional, we investigate a novel application of isotonic regression as an estimator of this variance function. Our proposal of variance estimation with isotonic regression is used in multiple classical regression problems focused on mean estimation and model validation. In a series of numerical examples, we (1) explore the power variance parameter of the variance function within Tweedie's family of distributions, (2) derive a semi-parametric bootstrap under heteroskedasticity, (3) provide a test for auto-calibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, (5) deal with several difficulties under lognormal assumptions. In all these problems we verify that the variance estimation with isotonic regression is essential for proper mean estimation and beneficial compared to traditional statistical techniques based on local polynomial smoothers.


Delong, Ł., Kozak, A., 2023, The use of autoencoders for training neural networks with mixed categorical and numerical features

Published Paper, 01-02-2023

We focus on modelling categorical features and improving predictive power of neural networks with mixed categorical and numerical features in supervised learning tasks. The goal of this paper is to challenge the current dominant approach in actuarial data science with a new architecture of a neural network and a new training algorithm. The key proposal is to use a joint embedding for all categorical features, instead of separate entity embeddings, to determine the numerical representation of the categorical features which is fed, together with all other numerical features, into hidden layers of a neural network with a target response. In addition, we postulate that we should initialize the numerical representation of the categorical features and other parameters of the hidden layers of the neural network with parameters trained with (denoising) autoencoders in unsupervised learning tasks, instead of using random initialization of parameters. Since autoencoders for categorical data play an important role in this research, they are investigated in more depth in the paper. We illustrate our ideas with experiments on a real data set with claim numbers, and we demonstrate that we can achieve a higher predictive power of the network.


Delong, Ł., Lindholm, M., Wüthrich, M.V., 2021, Gamma Mixture Density Networks and their application to modelling insurance claim amounts

Published Paper, 05-10-2021

We discuss how mixtures of Gamma distributions with mixing probabilities, shape and rate parameters depending on features can be fitted with neural networks. We develop two versions of the EM algorithm for fitting so-called Gamma Mixture Density Networks, which we call the EM network boosting algorithm and the EM forward network algorithm, and we test their implementation together with the choices of hyperparameters. A simulation study shows that our algorithms perform very well on synthetic data sets. We further illustrate the application of the Gamma Mixture Density Network on a real data set of motor insurance claim amounts and conclude that Gamma Mixture Density Networks can improve the fit of the regression model and the predictions of the claim severities used for rate-making compared to classical actuarial techniques.


  • 2022, Virtual Orlando Actuarial Colloquium, Gamma Mixture Density Networks and their application to insurance modelling claim amounts

  • 2022, 73rd Joint Lyon-Lausanne Actuarial Seminar, Lausanne, Switzerland, One-year and ultimate premium and reserve risks (invited talk)

  • 2022, 11th Conference in Actuarial Science and Finance, Samos, Greece, Gamma Mixture Density Networks and their application to insurance modelling claim amounts (invited talk)

Read more


Adres e-mail:

  • Łukasz Delong
    44/50 Dluga street, 00-241 Warsaw
    Room: B311
    Consultancy hours: please send an e-mail