A Dynamic Investment Model with Control on the Portfolio's Worst Case Outcome
研究了一种控制下行损失的投资组合问题，通过将最差情形结果纳入目标函数，将投资问题转化为期权定价模型，并利用Black-Scholes公式得到闭式解。
This paper considers a portfolio problem with control on downside losses. Incorporating the worst‐case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black‐Scholes formula, a closed‐form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model.