Comonotonic Approximations for Optimal Portfolio Selection Problems
研究了Black-Scholes市场中多期投资组合选择问题，针对恒定混合策略，提出基于共单调性的精确近似方法，避免模拟计算，适用于目标资本积累和未来支付义务两类场景。
We investigate multiperiod portfolio selection problems in a Black and Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of “constant mix” portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari's dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene et al. (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically.