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 Associate Professor at SGH Warsaw School of Economics. I have PhD in Mathematics and Habilitation Degree in Economics. I am an actuary with license no. 130 issued by the Polish Financial Supervisor and Vice-President 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.


01.05.21 – New actuarial programmes at SGH will start the next academic year

15.04.21 – New version of my paper on Gamma Mixture Density Networks is available

10.04.21 – My new paper on one-year and ultimate reserve risk is available

  • May 2013

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

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

  • October

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

    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

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

    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, claims reserving, non-life ratemaking, loss distributions, loss curve fitting, Monte Carlo simulations and pricing of derivatives.

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 applications.

From GLMs to Neural Networks

Non-life ratemaking, loss distribution modeling, individual claims reserving and credit risk...

I have deep knowledge and experience in applying Generalized Linear Models and Generalized Additive Models in actuarial and non-actuarial applications, including non-life ratemaking, loss distribution modeling and credit risk. Recently, I have been attracted with individual claims reserving and I am developing my skills in machine learning techniques and neural networks.

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

Working 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.


Delong, Ł., Wüthrich, M.V., 2020, Neural networks for the joint development of individual payments and claim incurred

Published Paper, 27-02-2020

The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims.


Delong, Ł., 2013, Backward Stochastic Differential Equations with Jumps and their Actuarial and Financial Applications

Book, 10-04-2013

Backward Stochastic Differential Equations with jumps can be used to solve problems in both finance and insurance.


This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.


  • 2020, Virtual Actuarial Colloquium, Neural networks for the joint development of individual payments and claim incurred

  • 2019, 23rd IME Conference, Munich, Germany, Fair valuation of insurance liability cash flow streams in continuous time

  • 2019, AFIR-ERM Colloquium, Florence, Italy, Fair valuation of insurance liability cash flow streams in continuous time

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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)