CS16: Recent Advances in Financial and Actuarial Mathematics

Dr

Joanna Janczura

We propose a new method for probabilistic forecasting of electricity prices. It is based on averaging point forecasts from different models combined with expectile regression. We show that deriving the predicted distribution in terms of expectiles, might be in some cases advantageous to the commonly used quantiles. Using expectile predictions as a future risk measure we propose a short-term diversification strategy for an electricity trader. The proposed methods are applied to the day-ahead electricity prices from the German market. The obtained results show that implementation of dynamic strategies based on expectiles improves the outcomes in terms of risk as well as profit.

Bibliography

\([1]\) Joanna Janczura. “Expectile regression averaging method for probabilistic forecasting of electricity prices.” Computational Statistics vol. 40, 2025, pp. 683–700.

\([2]\) Joanna Janczura, Edyta Wójcik. “Dynamic short-term risk management strategies for the choice of electricity market based on probabilistic forecasts of profit and risk measures. The German and the Polish market case study.” Energy Economics vol. 110, 2022, pp. 106015.

Valuation of multi-region CoCoCat bonds

Krzysztof Burnecki

We introduce a novel, multidimensional insurance-linked instrument: a contingent convertible bond (CoCoCat bond) whose conversion trigger is activated by predefined natural catastrophes across multiple geographical regions. We develop such a model, explicitly accounting for the complex dependencies between regional catastrophe losses. Specifically, we explore scenarios ranging from complete independence to proportional loss dependencies, both with fixed and random loss amounts. Utilizing change-of-measure techniques, we derive risk-neutral pricing formulas tailored to these varied dependence structures. By fitting our model to real-world natural catastrophe data from Property Claim Services, we demonstrate the significant impact of inter-regional dependencies on the CoCoCat bond’s pricing, highlighting the importance of multidimensional risk assessment for this innovative financial instrument.

Expectiles in probabilistic forecasting of electricity prices with risk management implications

Joanna Janczura

We propose a new method for probabilistic forecasting of electricity prices. It is based on averaging point forecasts from different models combined with expectile regression. We show that deriving the predicted distribution in terms of expectiles, might be in some cases advantageous to the commonly used quantiles. Using expectile predictions as a future risk measure we propose a short-term diversification strategy for an electricity trader. The proposed methods are applied to the day-ahead electricity prices from the German market. The obtained results show that implementation of dynamic strategies based on expectiles improves the outcomes in terms of risk as well as profit.

Bibliography

\([1]\) Joanna Janczura. “Expectile regression averaging method for probabilistic forecasting of electricity prices.” Computational Statistics vol. 40, 2025, pp. 683–700.

\([2]\) Joanna Janczura, Edyta Wójcik. “Dynamic short-term risk management strategies for the choice of electricity market based on probabilistic forecasts of profit and risk measures. The German and the Polish market case study.” Energy Economics vol. 110, 2022, pp. 106015.

Implicit control for L'evy-type dividend-impulse problem

Zbigniew Palmowski

Assume the capital or surplus of an insurance company evolves randomly over time as the spectrally negative Lévy process but where in addition the company has the possibility to pay out dividends to shareholders and to inject capital at a cost from shareholders. We impose that when the resulting surplus becomes negative the company has to decide whether to inject capital to get to a positive surplus level in order for the company to survive or to let ruin occur. The objective is to find the combined dividends and capital injections strategy that maximises the expected paid out dividends minus cost of injected capital, discounted at a constant rate, until ruin. We consider the setting where the cost of capital is level-dependent in the sense that it is higher when the surplus is below \(0\) than when it is above \(0\). We investigate optimality of a \(3\)-parameter strategy with parameters \(-r < 0 < c < b\) where dividends are paid out to keep the surplus below \(b\), capital injections are made in order to keep the surplus above \(c\) unless capital drops below the level \(-r\) in which case the company decides to let ruin occur. The proof is based on some monotonicity properties for the solution of the renewal equation with log-convex kernel.