Pricing corporate securities with noisy asset information

We consider the pricing of corporate securities when investors do not have full information. One approach for this is to consider a random default boundary, such that even if the firm value was known, the time of default would not be predictable. On the other side, in reality investors do not have access to the true firm value. This is taken into account using an approach which considers the firm value unobservable and uses noisy information to obtain a filter problem. The filter problem is solved approximately and consequences to the pricing of equity and debt are examined.