In this paper, we study the optimal financing problem in the dual model. We introduce a value function which considers both the expected present value of the dividends payout minus the equity issuance and a penalty at...In this paper, we study the optimal financing problem in the dual model. We introduce a value function which considers both the expected present value of the dividends payout minus the equity issuance and a penalty at ruin. In order to get the optimal strategy,two categories of suboptimal models are constructed and studied. Based on these two suboptimal models, we identify the value function and the optimal strategy in the general optimal problem.展开更多
In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an a...In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11361007)the Guangxi Natural Science Foundation(Grant No.2014GXNSFCA118001)+3 种基金the Fostering Project of Dominant Discipline and Talent Team of Shandong Provincial Higher Education Institutionsthe Fostering Project of Dominant Discipline and Talent Team of SDUFEProject of Shandong Provincial Higher Educational Science and Technology Program(Grant Nos.J15LI01J17KA163)
文摘In this paper, we study the optimal financing problem in the dual model. We introduce a value function which considers both the expected present value of the dividends payout minus the equity issuance and a penalty at ruin. In order to get the optimal strategy,two categories of suboptimal models are constructed and studied. Based on these two suboptimal models, we identify the value function and the optimal strategy in the general optimal problem.
文摘In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.
