This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optima
l stopping time problem with state constraint, and then in a Markovian setting, we investigate the optimal strategy by analyzing the properties of the corresponding free boundary, including its position, asymptotics, monotonicity and regularity. We identify situations when call precedes conversion, and vice versa. Moreover, we show that the irregular payoff results in the possibly non-monotonic conversion boundary. Surprisingly, the price of the convertible bond is not necessarily monotonic in time: it may even increase when time approaches maturity.
Laser induced ultrafast demagnetization in ferromagnetic metals was discovered almost 20 years ago, but currently there is still lack of consensus on the microscopic mechanism responsible for the corresponding transfer of angular momentum and energy
between electron, lattice and spin subsystems. A distinct, but intrinsically correlated phenomenon occurring on a longer timescale is the magnetization precession after the ultrafast demagnetization process, if a magnetic field is applied to tilt the magnetization vector away from its easy direction, which can be attributed to the change of anisotropy after laser heating. In an in-plane magnetized Pt/Co/Pt thin film with perpendicular interface anisotropy, we found excellent agreement between theoretical prediction with plausible parameters and experimental data measured using time resolved magneto-optical Kerr effect. This agreement confirms that the time evolution of the anisotropy field, which is driven by the interaction between electrons and phonons, determines the magnetization precession completely. A detailed analysis shows that, even though the whole sample is magnetized in-plane, the dynamic interface anisotropy field dictates the initial phase of the magnetization precession, highlighting the significance of the interface anisotropy field in laser induced magnetization precession.
We develop a self-consistent theory for current-induced spin wave excitations in normal metal-magnetic insulator bilayer systems, thereby establishing the relation between spin wave excitation and the experimentally controlled parameters. We fully ta
ke into account the complex spin wave spectrum including dipolar interactions and surface anisotropy as well as the spin-pumping at the interface. Our results focus on the mode-dependent power close to the critical currents for spin wave excitation. The major findings are (a) the spin transfer torque can excite different spin-wave modes simultaneously; (b) spin pumping counterbalances spin-transfer torque and affects the surface modes more than the bulk modes; (c) spin pumping inhibits high frequency spin-wave modes, thereby redshifting the excitation spectrum. We can get agreement with experiments on yttrium iron garnet|platinum bilayers by postulating the existence of surface anisotropy modes.
