The present paper investigates an optimal reinsurance-investment problem with Hyperbolic Absolute Risk Aversion (HARA) utility. The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer. The insurer is allowed to purchase reinsurance from the reinsurer. Both the insurer and the reinsurer are assumed to invest in one risk-free asset and one risky asset whose price follows Heston's SV model. Our aim is to seek optimal investment-reinsurance strategies to maximize the expected HARA utility of the insurer's and the reinsurer's terminal wealth. In the utility theory, HARA utility consists of power utility, exponential utility and logarithmic utility as special cases. In addition, HARA utility is seldom studied in the optimal investment and reinsurance problem due to its sophisticated expression. In this paper, we choose HARA utility as the risky preference of the insurer. Due to the complexity of the structure of the solution to the original Hamilton-Jacobi-Bellman (HJB) equation, we use Legendre transform to change the original non-linear HJB equation into its linear dual one, whose solution is easy to conjecture in the case of HARA utility. By calculations and deductions, we obtain the closed-form solutions of optimal investment-reinsurance strategies. Moreover, some special cases are also discussed in detail. Finally, some numerical examples are presented to illustrate the impacts of our model parameters (e.g., interest and volatility) on the optimal reinsurance-investment strategies.

This paper is devoted to study a robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks for an ambiguity-averse insurer (AAI). Assume that the AAI's wealth process consists of two p-thinning dependent classes of insurance business. The AAI is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, where risky asset's price follows CEV model. Under the criterion of maximizing the expected exponential utility of AAI's terminal wealth, the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy are derived by employing techniques of stochastic control theory. Moreover, we provide the verification theorem and present some numerical examples to analyze the impacts of parameters on our optimal control strategies.

An automatic document feeder (ADF) is an important part of a copier, which is capable of feeding a document for double-sided scanning, includes mechanical structure and control system. Control system is the core unit, which is responsible for original feeding, original separation, original registration, original conveyance, etc. Control system will directly affect the accuracy of machine efficiency. In order to design control system, mathematical model should be welldesigned first. The original-feeding system of an ADF is controlled and validated in this paper. The ADF studied here is a prototype developed by Konica, a company that develops professional printing systems. We construct a model of original-feeding system for the ADF in Simulink, and software which is using for modeling dynamic system, simulating and analyzing, and express the PID gains. Next, we contrast original feed motor's speed on real condition to simulation results for checking whether the PID gains are reasonable. The comparison shows the upward trend in motor speed is similar, and the actual rise time is shorter. The reason for that is: the test data on real condition focus on the moment when the original feeds in, all the loads involved in simulation are not added to motion control system. In this sense, in addition to finding better PID gains in the ADF motion control system, our analysis also led to a better understanding of system.