Optimal control of investment in a collective pension insurance model: study of singular nonlinear problems for integro-differential equations

For a collective pension insurance model (dual risk model), the optimal control of investments aimed at maximizing the survival probability of an insurance company is considered. The search for an optimal strategy by applying dynamic programming leads to singular nonlinear boundary value problems for integro-differential equations. In the case of an exponential premium size distribution, these problems are studied analytically. Numerical results are presented and compared with previous computations in the case of simple investment strategies (risky and risk-free) in the considered model.