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In the classic dividend surplus model, initial surplus are generally fixed and premiums or incomes increased linearly. In our research, we consider that the initial surplus and income in the Erlang(2) dividend model will also change over time. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. In this paper, we adopt Statistical methods to convert the differential equations with variable coefficients to ordinary differential equation and further study the optimal periodic barrier strategies when the initial surplus is dynamic and the income is nonlinear under the condition of the inter-dividend decision times follow Erlang(2) distribution.

This paper mainly studies the optimal investment problem of defined contribution (DC) pension under the self-protection and minimum security. First, we apply [see formula in PDF] theorem to obtain the differential equation of the real stock price after discounting inflation. Then, under the constraint of external guarantee of DC pension terminal wealth, self-protection is introduced to study the maximization of the expected utility of terminal wealth at retirement time and any time before retirement. The explicit solution of the optimal investment strategy of DC pension at retirement time and any time before retirement should be derived by martingale method. Finally, the influence of self-protection on the optimal investment strategy of DC pension is numerically analyzed.

Under the S-shaped utility of loss aversion, this paper considers the bequest motivation of pension plan participants, random salary income before retirement and the substitution rate between receiving pension benefits after retirement and wages before retirement, and studies the optimal investment strategy of defined contribution (DC) pension. Assuming that pension funds can invest in a financial market consisting of three assets (risk-free asset cash, rolling bonds and stocks), inflation is considered by discount. Under the S-shaped utility, the Lagrange method is used to find the terminal optimal surplus of pensions in retirement, so as to find the terminal optimal wealth, and then the martingale method is used to find the optimal wealth process and investment strategy. Finally, a sensitivity analysis is carried out on the the influence of bequest motivation and loss aversion on the optimal investment strategy of DC pension.

In recent years, it is of great interest to evaluate the level of liabilities of the hybrid pension system as the mixed pension schemes are favored by various countries around the world. This paper further improves the hybrid pension liability assessment method proposed by Broeders et al by accounting for inflation risk and assuming that inflation risk is measured by a price index that follows geometric Brownian motion. A simulation-based pricing framework is then introduced to assess the hybrid pension liability. The results show that the introduction of inflation risk increases the total outstanding liability of hybrid pensions. Furthermore, inflation is negatively correlated with the total outstanding liability of the hybrid pension scheme, while inflation volatility is positively correlated with it.