In this paper, we model the insurance company's surplus flow by a perturbed compound Poisson model. Suppose that at a sequence of random time points, the insurance company observes the surplus to decide dividend payments. If the observed surplus level is larger than the maximum of a threshold b > 0 and the last observed level (after dividends payment if possible), then a fraction 0 < θ < 1 of the excess amount is paid out as a lump sum dividend. We assume that the solvency is also discretely monitored at these observation times, so that the surplus process stops when the observed value becomes negative. Integro-differential equations for the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function are derived, and solutions are also analyzed by Laplace transform method. Numerical examples are given to illustrate the applicability of our results.

We investigate a portfolio optimization problem in a continuous-time Markov-modulated financial market. The unobservable mean return of a risky asset follows a continuous-time, two-state Markov chain whose states are interpreted as different states of market. Using results from filter theory, we reduce this problem to one with complete observation. We solve the problem by stochastic control methods and the optimal portfolio can be explicitly characterized by stochastic integrals. The Monte Carlo simulations are implemented to compute the optimal portfolio allocations. The results show that state uncertainty have a great influence on optimal portfolio choice. The parameter uncertainty prompts the investor to hedge against unanticipated changes in the state variables.

In order to find the causes of price volatility in bond futures market, we consider the potential impact of trading properties and construct a multivariate linear model between realized volatility and Behavioral variables included the strategies of Open, Close, Long, Short and turnover. Then through an empirical analysis of tick-by-tick data, we found that realized volatility is negative respectively related to Long, Double-close and turnover, and positive correlated to Long-Close, Shot and shot-Close. The double-turnover has weakly influence, and both sides explain differences. The volume is not significantly explaining the price volatility. Therefore, our findings will be helpful to manage the risk of bond futures transactions.