Preventing successive bankruptcies of financial institutions by impulse control

Preventing successive bankruptcies of financial institutions by impulse control

Since default problem in financial contracts and risk caused by the default have been analyzed more accurate in last years, measurement, prediction and control of the default have become more important. In this article, investor is central bank that allocates its wealth in three types of assets on a finite time horizon [0, T] : a money market account, a stock, and defaultable securities. In fact central bank buys defaultable securities from financial institutions under its control. Or, in other words, the central bank give a loan to these institutions at a specified rate. Since default probability exists for financial institutions, we consider a threshold as default threshold and the time which Hazard process of each of these institutions goes beyond this threshold, we call alarm time. It is important to control the Hazard process of a financial institution that, in the event of a default of one of the financial institutions under the control of the central bank, the other institutions also begin to default. These defaults happen like a domino game. Continuing this trend, will cause a big disruption in the banking system of a country. In our article, the control of Hazard process of financial institutions be analyzed using impulse control tool. Our suggestion to prevent default of financial institutions is that the central bank can prevent default of financial institutions by inject liquidity to these institutions be in close times to the default time. This control be modeled by impulse control. The goal of this article to provide optimal impulse control including optimal transaction times and the optimal amount of this moneys for maximizing expected central bank utility from the wealth of the portfolio.

Since default problem in financial contracts and risk caused by the default have been analyzed more accurate in last years, measurement, prediction and control of the default have become more important. In this article, investor is central bank that allocates its wealth in three types of assets on a finite time horizon [0, T] : a money market account, a stock, and defaultable securities. In fact central bank buys defaultable securities from financial institutions under its control. Or, in other words, the central bank give a loan to these institutions at a specified rate. Since default probability exists for financial institutions, we consider a threshold as default threshold and the time which Hazard process of each of these institutions goes beyond this threshold, we call alarm time. It is important to control the Hazard process of a financial institution that, in the event of a default of one of the financial institutions under the control of the central bank, the other institutions also begin to default. These defaults happen like a domino game. Continuing this trend, will cause a big disruption in the banking system of a country. In our article, the control of Hazard process of financial institutions be analyzed using impulse control tool. Our suggestion to prevent default of financial institutions is that the central bank can prevent default of financial institutions by inject liquidity to these institutions be in close times to the default time. This control be modeled by impulse control. The goal of this article to provide optimal impulse control including optimal transaction times and the optimal amount of this moneys for maximizing expected central bank utility from the wealth of the portfolio.