Abstract: In this paper, an innovative financing instrument called contingent convertible security (CCS) is introduced. Using the optimal control, optimal stopping and real options theory, the optimal investment and financing decisions of a firm that issues CCS together with equity and the straight bond is examined. The risk-neutral prices of all the corporate securities, ruin probability within a given time horizon and optimal capital structure are provided. It's shown that there is an optimal fraction of equity allocated to the CCS holders upon conversion that eliminates the agency cost of debt. The optimal fraction is given explicitly. The numerical simulation is performed and static comparative analysis is provided. The numerical examples prove the rationality of the model and the validity of conclusions. In particular, It's demostrated the new invented CCS can significantly increase the value of the option to invest. In contrast to the standard capital structure that issues equity and the straight bond only, issuing CCS can lead to as much as 11.5 percent increase in the real option's value but the number declines to 7.4 percent if the contingent convertible bond is issued instead of CCS. CCS decreases bankruptcy risk as well as the yield spread of the straight bond. With a growth of the volatility rate of the investment project, the issuing firm will increase the investment trigger, the amount of CCS issued, instead of the straight bond and the firm's leverage.

Key words: contingent capital, real options, capital structure, optimal stopping