Evolutionary Portfolio Selection with Liquidity Shocks

Insurance companies invest their wealth in financial markets. The wealth evolution strongly depends on the success of their investment strategies, but also on liquidity shocks which occur during unfavourable years, when indemnities to be paid to the clients exceed collected premia. An investment strategy that does not take liquidity shocks into account, exposes insurance companies to the risk of bankruptcy, when liquidity shocks and low investment payoffs jointly appear. Therefore, regulatory authorities impose solvency restrictions to ensure that insurance companies are able to face their obligations with high probability. This paper analyses the behaviour of insurance companies in an evolutionary framework. We show that an insurance company that merely satisfies regulatory constraints will eventually vanish from the market. We give a more restrictive no bankruptcy condition for the investment strategies and we characterize trading strategies that are evolutionary stable, i.e. able to drive out any mutation.