Dynamic Analysis of Hydro-Turbine Governing System with Multistochastic Factors

This paper explores the stability of a hydro-turbine governing system (HTGS) under simultaneous effects of multistochastic factors. Specifically, three different sets of stochastic factors are introduced into the governing system, and the corresponding mathematical model with multistochastic factors is proposed. Then, seven cases are performed to reveal the dynamic characteristics of the governing system, including the excitations of only single stochastic factor, two stochastic factors, and three stochastic factors with different combinations of stochastic parameters. The results show some interesting phenomena. First, the stability of the system is weakened by introducing stochastic variables ω2 and ω3 into the inlet pressure of hydro-turbine (h2) and the bottom pressure of the surge tank (h3) separately, or both. Second, the negative effects of the stochastic characteristics of h2 and h3 on the governing system are reduced by introducing the stochastic variable (ω1) into the hydro-turbine flow (q1), on the basis of fully considering the influence of the stochastic characteristics of h2 and h3. Third, stochastic factors are generally considered to be unfavorable, but it may help the system to reach a global optimum status under certain conditions, which break through the habit of empirical thinking. Finally, this work not only provides a new insight for stochastic phenomena existing in engineering system, but also lays a theoretical basis for the safe and stable operation of the hydropower stations.

Optimal Excess-of-Loss Reinsurance for Stochastic Factor Risk Models

We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer’s surplus is governed by a marked point process with dual-predictable projection affected by an environmental factor and that the insurance company can borrow and invest money at a constant real-valued risk-free interest rate r. Our model allows for stochastic risk premia, which take into account risk fluctuations. Using stochastic control theory based on the Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy under the criterion of maximizing the expected exponential utility of the terminal wealth. A verification theorem for the value function in terms of classical solutions of a backward partial differential equation is provided. Finally, some numerical results are discussed.