In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injec...In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.展开更多
With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reductio...With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.展开更多
This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential ra...This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.展开更多
We study a quasilinear elliptic equation with polynomial growth coefficients. The existence of infinitely many solutions is obtained by a dual method and a nonsmooth critical point theory.
基金Supported by the National Natural Science Foundation of China(11231005)Promotive research fund for excellent young and middle-aged scientists of Shandong Province(BS2014SF006)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(15KJB110009)
文摘In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.
基金Supported by the Fundamental Research Funds for the Central Universities(2013XK03)the National Natural Science Foundation of China under Grant No.11371361
文摘With the help of some reductions of the self-dual Yang Mills(briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of(2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation,the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new(2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of(2 + 1)-dimensional integrable couplings of a new(2 + 1)-dimensional integrable nonlinear equation.
基金Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093)。
文摘This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.
基金supported in part by the National Natural Science Foundation of China(11261070)
文摘We study a quasilinear elliptic equation with polynomial growth coefficients. The existence of infinitely many solutions is obtained by a dual method and a nonsmooth critical point theory.
