Precommitted Investment Strategy versus Time-Consistent Investment Strategy for a Dual Risk Model

Abstract EN

We are concerned with optimal investment strategy for a dual risk model.

We assume that the company can invest into a risk-free asset and a risky asset.

Short-selling and borrowing money are allowed.

Due to lack of iterated-expectation property, the Bellman Optimization Principle does not hold.

Thus we investigate the precommitted strategy and time-consistent strategy, respectively.

We take three steps to derive the precommitted investment strategy.

Furthermore, the time-consistent investment strategy is also obtained by solving the extended Hamilton-Jacobi-Bellman equations.

We compare the precommitted strategy with time-consistent strategy and find that these different strategies have different advantages: the former can make value function maximized at the original time t=0 and the latter strategy is time-consistent for the whole time horizon.

Finally, numerical analysis is presented for our results.