Abstract
We consider an insurer who faces an external jump-diffusion risk that is negatively correlated with the capital returns in a multidimensional regime switching model. The insurer selects investment and liability ratio policies continuously to maximize her/his expected utility of terminal wealth. We obtain explicit solutions of optimal policies for logarithmic and power utility functions. We study the impact of the insurer’s risk aversion, the negative correlation between the external risk and the capital returns, and the regime of the economy on the optimal policy. We find, among other things, that the regime of the economy and the negative correlation between the external risk and the capital returns have a dramatic effect on the optimal policy.
Highlights
To further illustrate how severe this financial crisis was, we review the staggering case of American International Group, Inc. (AIG), once one of the largest and most successful insurance companies in the world
We always have: π1∗ > π2∗ and κ1∗ > κ2∗. This result shows that all insurers, regardless of risk aversion, should invest a greater proportion in the risky asset and choose a higher liability ratio when the economy is in the bull regime
AIG ignored the negative correlation between its liabilities and the capital gains in the financial market
Summary
The 2007–2009 financial crisis and economic recession almost put the global financial system on the brink of collapse. AIG’s stock price was traded at over $50 per share in February 2008 before the financial crisis, but dropped to less than $2 per share in September 2008 when AIG was deep in the crisis. To prevent the financial system from breakdown, the U.S government took over AIG through an initial rescue of $85 billion in September. The total amount of rescue in the AIG case is over $182 billion (see [2] for additional information). Many academics investigate the influence of complicated financial products, such as credit default swaps (CDS), on the economy and the financial system. They debate over monetary policies, government intervention, regulation of the markets, systemic risk, etc. There are still many important open problems on quantitative investment and risk management with regards to the financial crisis, e.g., the mechanism of contagion effects in financial market; pricing, hedging and investing under systemic influences and complex dependence; and systemic risk measure
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