Optimal dividends under a stochastic interest rate

Optimal dividends in the dual risk model under a stochastic interest rate

“…From the discussions above, we find the optimal dividends strategies in dual risk models under stochastic interest rates, assuming the discounting factor is a geometric Brownian motion or exponential Lévy process. The strategies are analogous to the ones discussed by Eisenberg [5]. In restricted case, where the dividends payment is bounded, the optimal strategy is a threshold strategy.…”

Optimal dividends with partial information and stopping of a degenerate reflecting diffusion

“…The literature on the optimal dividend problem is very rich with seminal mathematical contributions by Jeanblanc and Shiryaev [32] and Radner and Shepp [42]. More recent contributions include, among many others, the survey by Avanzi [2], Akyildirim et al [1] and Eisenberg [23] who consider random interest rates, Avram et al [3] who allow jumps in the dynamics of X, Jiang and Pistorius [33] who consider a regime-switching dynamics for the coefficients in (1.1), or Bayraktar et al [6] who consider jumps in the dynamics of X and fixed transaction costs for dividend lump payments. However, research so far has largely focused on explicitly solvable examples.…”

The Optimal Dividend Payout Model with Terminal Values and Its Application

“…From the construction above, it is easily to verify that the expressions (59)-(61) are solutions to (14) and (15). In addition, the proof on concavity of ( ) is similar to that of Theorem 2.1 in Højgaard and Taksar [29], so we omit it here.…”

“…Although the HJB equation (14) with the mixed boundary condition (100) cannot be solved in a straightforward manner, we can establish a relation between ( ) and ( ), in which the boundary condition (100) is replaced by (15), by comparing it with the nonzero terminal bankruptcy problem.…”

“…Recently, diffusion models for firms with controllable risk exposure and dividends payout have drawn increasing attention of researchers. We refer the readers to Jeanblanc-Picqué and Shiryaev [2], Radner and Shepp [3], Taksar and Zhou [4], Højgaard and Taksar [5,6], Hubalek and Schachermayer [7], Cadenillas et al [8], Paulsen [9,10], Paulsen and Gjessing [11], Avanzi and Wong [12], Hunting and Paulsen [13], Chen et al [14], Eisenberg [15], Vierkötter and Schmidli [16], and so forth. In all of those works, the terminal value of a company is assumed to be equal to zero when there is a status of bankruptcy, where the bankruptcy is defined as the time when the liquid assets of the company vanish.…”