Game Pricing For Perpetual Convertible Bond With Credit Risk

In this paper,we consider the stock price of the company as the underlying as-sets,and use the method of the diferential equation.From the aspects of issuer andinvestor,we consider the pricing of the perpetual convertible bond with credit risk.Wefrst raise the optimal stopping game problem in the context of a reduced form modeldriven by a Brownian motion and a compound Poisson process with power jump-s.We notice that,calls and conversions often occur far from maturity,so we just modelthis situation with a perpetual convertible bond.Then we also raise a free boundaryproblem,and give an explicit solution to it with some fgures.Last,we prove that thissolution is exactly the solution of the optimal stopping game.It turns out that theoptimal stopping strategies whose structure difers from the compensation whichpay by issuer for recall the bond.