Optimal Asset Allocation for Participating Contracts under Short-Selling and VaR Constraints ----- Based on the Dual Perspective of the Insurer and the Insured

From the dual perspective of the insurer and the insured, we investigate an optimal investment problem with short-selling and two-VaR constraints faced by the insurer who offers participating contracts. This analysis is particularly relevant for an insurance company operating under the Solvency II regulation which aims to maximize the expected utility of the terminal payoff to the insurer, while at the same time being required to provide its policyholders a minimum guaranteed amount and a bonus. We adopt a dual control approach and a concavification technique to solve the problem and derive the representations of the optimal terminal wealth. We also carry out some numerical analysis to show that in contrast to one-VaR constraint that we consider only from the perspective of the insurer or the insured, two-VaR constraint that we consider from the dual perspective can strictly improve the risk management for bad economic states and decrease the moral risk.