# 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 in insurance. I am Editor of ASTIN Bulletin – The Journal of International Actuarial Association.

### Highlights:

10.07 – I will be giving a presentation at IME Conference in Munich

24.05-My presentation won the award for the best paper presented in AFIR-ERM Colloquium in Florence, read the paper

20.05 – I received a grant from the National Science Center, see the project

## Curriculum Vitae

• 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
2007

#### 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)

## Interests

#### 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.

## Publications

### Delong, Ł., Dhaene, J., Barigou, K., 2019, Fair valuation of insurance liability cash-flow streams in continuous time: Theory

Published Paper, 05-03-2019

We investigate fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. We first consider one-period hedge-based valuations, where in the first step, an optimal dynamic hedge for the liability is set up, based on the assets traded in the market and a quadratic hedging objective, while in the second step, the remaining part of the claim is valuated via an actuarial valuation. Then, we extend this approach to a multi-period setting by backward iterations for a given discrete-time step $h$, and consider the continuous-time limit for $h\to 0$. We formally derive a partial differential equation for the valuation operator which satisfies the continuous-time limit of the multi-period, discrete-time iterations and prove that this valuation operator is actuarial and market-consistent. We show that our continuous-time fair valuation operator has a natural decomposition into the best estimate of the liability and a risk margin. The dynamic hedging strategy associated with the continuous-time fair valuation operator is also established. Finally, the valuation operator and the hedging strategy allow us to study the dynamics of the net asset value of the insurer.

### Delong, Ł., 2019, Asymptotic optimality of a first-order approximate strategy for an exponential utility maximization problem with a small coefficient of wealth-dependent risk aversion

Working Paper, 02-01-2019

In Delong (2019) we investigate an exponential utility maximization problem for an insurer who faces a stream of non-hedgeable claims. We assume that the insurer's risk aversion coefficient consists of a constant risk aversion and a small amount of wealth-dependent risk aversion. We apply perturbation theory and expand the equilibrium value function of the optimization problem on the parameter $\epsilon$ controlling the degree of the insurer's risk aversion depending on wealth. We derive a candidate for the first-order approximation to the equilibrium investment strategy. In this paper we formally show that the zeroth-order investment strategy $\pi_0^*$ postulated by Delong (2019) performs better than any strategy $\pi_0$ when we compare the asymptotic expansions of the objective functions up to order $\mathcal{O}(1)$ as $\epsilon\rightarrow 0$, and the first-order investment strategy $\pi_0^*+\pi_1^*\epsilon$ postulated by Delong (2019) is the equilibrium strategy in the class of strategies $\pi^*_0+\pi_1\epsilon$ when we compare the asymptotic expansions of the objective functions up to order $\mathcal{O}(\epsilon^2)$ as $\epsilon\to 0$, where $\epsilon$ denotes the parameter controlling the degree of the insurer's risk aversion depending on wealth.

### 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.

## Conferences

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

• 2018, Workshop for Young Mathematicians organized by German Society of Actuaries, Ulm, Germany, Fair valuation of insurance liability cash flow streams in continuous time (invited talk)

• 2018, Actuarial and Financial Mathematics Conference, Brussels, Belgium, Time-inconsistent optimization problems in insurance and finance (invited talk)