Financial decision making under optimal control and Markov switching double exponential jump process

The purpose of this paper is two-fold. First, it lies in studying how to value a perpetual real option to be invested in a project that results in the creation of a new firm, whose financing scheme is composed of equity, standard debt, and contingent convertible debt. This occurs when the volatility of cash flows is captured by an exponential double-jump stochastic process and where the economic situation is represented by a continuous stochastic switching regime. In fact, the expected return of the project is governed by a continuous-time two-state Markov chain since the recurrent and discontinuous switching regime of the economy is alternating between economic recession and boom environments. Second, it resides in assessing the financial solidity of the firm through considering a stopping time option to be invested by resolving an optimal control problem. In addition, we equally aim at coping the asymmetric information problem through considering a contingent convertible debt in the firm financial structure, which is transformed into stocks for a given threshold of the market value of the firm. This would yield the alignment of bondholders' interests with those of shareholders. A sensitivity analysis would allow us to compare the effects of different sources of financing on the value of the firm.