Optimal Dividend Policies Under Ruin Probability

With the development of the global economy,the problem of optimal dividends and capital injections has attracted extensive research in recent years,and in the actual investment market,capital injections play an important role in asset management.In our model,we study the problem of optimal dividends where profitability is stochastic under insolvency constraints.Firms face a trade-off between potential insolvency and profit extraction.The occurrence of bankruptcy is the main difficulty in our analysis.In particular,there are at least two free bounds in our problem,and we use dynamic programming principles to derive the HJB equation,which has a downward gradient constraint and cannot be solved analytically so far.We have carried out numerical simulations to give a numerical analysis of it.In contrast to previous work,we have replaced the Ornstein-Uhlenbeck model with a 3/2 volatility model with mean-reverting properties.We prove the continuity theorem for the value function and the Hamilton-Jacobi-Bellman equation given by dynamic programming.The Euler-Maruyama method and the Milstein method are used to computationally simulate the corresponding volatility processes.Finally,numerical calculations of the variational inequality equations satisfied by the value function are carried out,and the numerical results show that voluntary liquidation is optimal when profitability decreases to a certain threshold.