A rm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold the bond, thereby collecting coupons, or to convert it to stock. The rm may at any time call the bond. Because calls and conversions usually occur far from maturity, we model this situation with a perpetual convertible bond, i.e, a convertible coupon-paying bond without maturity. This model admits a relatively simple solution, under which the value of the perpetual convertible bond, as a function of the value of the underlying rm, is determined by a nonlinear ordinary dierential equation
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