Łukasz Delong SGH

Łukasz Delong

SGH Warsaw School of Economics Collegium of Economic Analysis Institute of Econometrics, Division of Probabilistic Methods

I am working as Full Professor at SGH Warsaw School of Economics. 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 neural networks in insurance. I am Editor of ASTIN Bulletin – The Journal of International Actuarial Association.


28.06.2022 – My first PhD student Marcin Szatkowski defended his thesis

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

27.12.2021 – I received a nomination for Professor of Economics and Finance conferred by the President of the Republic of Poland

  • 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

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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., Kozak, A., 2021, The use of autoencoders for training neural networks with mixed categorical and numerical features

Working Paper, 01-11-2021

We focus on modelling categorical features and improving predictive power of neural networks with mixed categorical and numerical features. First, we study regular and denoising autoencoders for categorical features in unsupervised learning problems. Second, we discuss possible architectures of neural networks in supervised learning problems which differ in the way categorical features are concatenated with numerical features. Third, we investigate a learning algorithm where we initialize parameters of a neural network in subsequent layers with representations of inputs learned with autoencoders for categorical and numerical data. We illustrate our techniques on a real data set with claim numbers. We conclude that our new architecture of a neural network initialized with parameters derived from autoencoders and a joint embedding for all categorical features performs better, in terms of predictive power, than the classical architecture with random initialization of parameters and separate entity embeddings for each categorical feature.


Delong, Ł., Szatkowski, M., 2021, One-year and ultimate reserve risk in Mack Chain Ladder model

Published Paper, 01-09-2021

We investigate the relation between one-year reserve risk and ultimate reserverisk in Mack Chain Ladder model in a simulation study. The first goal is to validate the so-called linear emergence pattern formula, which maps the ultimate loss to the one-year loss, incase when we measure the risks with Value-at-Risk. The second goal is to estimate the true emergence pattern of the ultimate loss, i.e. the conditional distribution of the one-year loss given the ultimate loss, from which we can properly derive a risk measure for the one-year horizon from the simulations of ultimate losses. Finally, our third goal is to test if classical actuarial distributions can be used for modelling of the outstanding loss from the ultimate and the one-year perspective. In our simulation study we investigate several synthetic loss triangles with various duration of the claims development process, volatility, skewness and distributional assumptions of the individual development factors. We quantify the reserverisks without and with the estimation error of the claims development factors.


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

Published Paper, 05-10-2020

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)

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Adres e-mail:

  • Łukasz Delong
    Madalińskiego 6/8, 02-513 Warsaw
    Room: 207, 209M
    Consultancy hours: IE SGH (please send an e-mail before the meeting)