Hedging derivatives: from finance to actuarial science

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The pricing, hedging and risk management of financial and insurance products have been key objects of study in over two decades. Although tremendous research efforts have addressed important aspects, there are still 'puzzles' yet to be solved. This research project focus on two main strands from the financial econometrics and actuarial science literature. The first part of the project investigates the pricing and hedging of financial derivatives, in particular options and volatility derivatives. Although a vast majority of the mathematical finance literature examines these in continuous time, mainly due to the tractability offered by this setup, quantities of interest are in general sampled at fixed dates and therefore, a discrete-time setting might be more appropriate. In this project we develop new methods for pricing and hedging of options and variance swaps based on a broad class of non-linear time series models and we illustrate the interplay with their continuous time limits, by studying the convergence between the corresponding quantities of interest. We further plan to investigate how these methods can be applied to hedging insurance products. In the second part of the proposal, we explore one of the major challenges faced by an insurance company regarding the quantification of its minimum required capital and its optimal investment into a well-diversified portfolio of financial assets. Motivated by the Solvency II Directives, we propose new optimization problems for non-life insurance companies, with different solvency constraints imposed by regulators. These optimization problems will be implemented in both static, and dynamic settings.