Conference Agenda

In order to appear reliable, insurance companies are interested in stabilising their surplus process and avoiding large losses. An object of interest is therefore the size of the drawdown, that is, the distance of the surplus to the last historical maximum. L. Brinker and H. Schmidli introduced the idea of dividing the size of the drawdown into a critical and a non-critical area. The aim is then to stabilise the drawdown in the non-critical area through a suitable reinsurance strategy. In reality, one can observe the process and adapt the strategy at discrete time points only. In this talk, we implement this idea by inspecting the drawdown process at the arrival times $\{T_k\}_{k\in\mathbb{N}}$ of a renewal process and by considering strategies of the form $$B_t = \sum_{k=0}^{\infty} b_k \mathbb{1}_{[T_k,T_{k+1})}(t)\;.$$ We then want to minimise the expected number of times at which a critical drawdown level is observed. In order to characterise the optimal strategy, we state a dynamic programming equation and show that the value function is the unique bounded solution. Moreover, the distribution of the drawdown under constant strategies can be calculated explicitly. This allows us to rewrite the dynamic programming equation into an integral form, which may be solved numerically. This talk is based on joint work with Hanspeter Schmidli.

We study the optimal bailout dividend problem with transaction costs for an insurance company, where shareholder payouts align with the arrival times of an independent Poisson process. In this scenario, the underlying risk model follows a spectrally negative L\'evy process. Our analysis confirms the optimality of a periodic $(b_{1},b_{2})$-barrier policy with classical reflection at zero. This strategy involves reducing the surplus to $b_1$ when it exceeds $b_{2}$ at the Poisson arrival times and pushes the surplus to 0 whenever it goes below zero.

Insurance companies and pension funds have asset-allocation processes that may involve multiple risk management constraints due to liabilities. Furthermore, the investment universe of such institutional investors often contains assets with different levels of liquidity, e.g., liquid stocks and illiquid investments in infrastructure projects or private equity. Therefore, we propose an analytically tractable framework for economic agents who maximize their expected utilities of terminal portfolio value by choosing investment-consumption strategies subject to lower bound constraints on both intermediate consumption and the terminal value of assets, some of which are liquid, while others are fixed-term. For institutional investors such as insurance companies consumption can be interpreted as payments to policyholders and/or dividends to shareholders.

In our talk, we present the key building blocks of our framework and demonstrate how to derive optimal investment-consumption strategies. At the end of the talk, we consider a numerical study, where we analyze optimal strategies from the economic perspective.