Risk-Based Approach for the Management of a Defined Benefit Pension Scheme

We apply a risk-based analysis to study the optimal investment-contribution-new venture strategy of a defined-benefit pension (DB) scheme. This problem is formulated as a zero-sum stochastic differential game (SDG) with jump-diffusion between the sponsor and the fictitious market. The scheme selects an optimal investment-contribution-new venture strategy that minimizes the risk described by a convex risk measure of the scheme's terminal wealth while the market selects a probability measure index analogous to the worst-case scenario where the risk is maximal. We apply the backward stochastic differential equation (BSDE) approach to solve the game problem. This allows us to obtain a simple and natural approach for the existence and uniqueness of an optimal strategy of the SDG without imposing any Markov assumptions